Vectors are often represented by directed line segments, with an initial point and a terminal point. Solution As we know that the resultant vector is given as: R = OA + OB +OC R = 5 + 10 + 15 R = 30N Example 2 Find out the resultant We know that force is a vector quantity, i.e., we need to specify both the magnitude and direction of a force to give its complete description. Now that we know what net force is, let us understand how to find the net force on an object. You can find the resultant for up to 2 force vectors. acting at a point and represented by the two sides of a parallelogram as shown in the figure. Net Force Calculator. The resultant vector is the vector that results from adding two or more vectors together. To your friends house, at the point (3, 4), imagine that you had to take two different roads these are the two red vectors. WebVector Calculator Solve vector operations and functions step-by-step Matrices Vectors full pad FAQ Examples Frequently Asked Questions (FAQ) What are vectors in math? Calculate and draw the resultant vector. A resultant vector is the result of either the addition, subtraction, multiplication, or division of two or more vectors to yield a new vector. The interaction of several force vectors on a body is an example of the resultant vector, and the resulting vector is obtained using this formula. Calculate the difference of vectors $v_1 = \left(\dfrac{3}{4}, 2\right)$ and $v_2 = (3, -2)$. How do I calculate a unit vector in the direction of another vector? This speeds and feeds calculator will help you set the rotation speed and feed rate of your machine tool, so you get fantastic results, whether you are drilling, milling, or boring. Yes! The cross product of vectors $ \vec{v} = (v_1,v_2,v_3) $ and $ \vec{w} = (w_1,w_2,w_3) $ is given by the formula: Note that the cross product requires both of the vectors to be in three dimensions. Net force definition, How to find net force Net force equation. WebTo calculate the magnitude of a 3D vector, a user enters in all 3 form fields, the vector's x, y, and z values. To find a unit vector in the direction of another vector v = (x, y, z), follow these steps: To find a vector of a specific magnitude in the direction of another vector v = (x, y, z): To find the magnitude and direction of two vectors, you must find the resultant vector (you can use our vector addition calculator to do it) and apply to it the steps described above. These vectors will be two sides of the parallelogram (not the opposite sides since they have the angle between them). Multiple vectors may be added together to produce a resultant vector. Math will no longer be a tough subject, especially when you understand the concepts through visualizations. This resultant is a single vector whose effect is equivalent to the net combined effect of the set of vectors that were added together. How to calculate the net force (formula with angles and formula with vector sum); Calculate the dot product of vectors $v_1 = \left(-\dfrac{1}{4}, \dfrac{2}{5}\right)$ and $v_2 = \left(-5, -\dfrac{5}{4}\right)$. An online resultant force calculator is presented. WebCalculate the resultant vector of three parallel forces pointing upwards. The units for net force are the same as the unit of force. Suppose there are three vectors in a plane, vector A, B and C. There resultant R can be calculated by adding all three vectors. The steps are quite straight forward. Check if the vectors are mutually orthogonal. This is an online calculator resultant force with the capability to calculate the resultant force of several forces, up to 4 in total in a concurrent force system. If you have three vectors e.g a, b, and c, first enter the a and b vectors and then add the resultant vector of a and b and the c vector. More in-depth information read at these rules. Example: the sum of (1,3) and (2,4) is (1+2,3+4), which is (3,7). How to find the resultant of more than three vectors? = 52 + 62 + 256Cos60 Now let us consider another case where the magnitude of the forces is the same as in the previous example, but now both the forces act in the same direction, i.e., 1=2=180\theta_1 = \theta_2 = 180 \degree1=2=180. \[ \vec {R}f = \vec {F}_1 + \vec {F}_2 + . \]. The subtraction of two vectors A and B can be derived from the formula A - B = A + (-B). its angle, from the positive direction of the ???x???-axis.. Learn about Vectors and Dot Products. They represent forces, velocities, In the XY plane, let A coordinate (a_x^0, b_y^0) and B coordinate (a_x^1 and b_x^1). So, the resultant vector is given as follow: Note: Vector addition is commutative in nature; the sum is independent of the order of addition. Answer: Hence the resultant of the two vectors is 12i + 9j - 15k. What is the sum of the two vectors? This new vector is defined as the resultant vector. They represent forces, velocities, and many other quantities derived from them. Resultant vector formula has numerous applications in physics, engineering. add the vector equations together to get the vector equation of Let v be a vector given in component form by. BYJU'S online resultant vector calculator 409+ PhD Experts 9.7/10 Ratings Vector Calculator. These formulas are for vectors in the same direction, for vectors in the opposite direction, and for vectors inclined to each other. WebThe resulting vector formula can be used in physics, engineering and mathematics. To draw the resultant vector, join the tail of the first vector with the second vectors head and put the arrowhead. The common types of vectors are cartesian vectors, column vectors, row vectors, unit vectors, and position vectors. Step 3: Finally, the resultant vector will be displayed in the output field. You can find the resultant for up to 2 force vectors. Step 2: Now click the button Calculate Resultant Vectors to get the result. A vector angle is the angle between two vectors in a plane. Formula 2 Vectors in the opposite direction are subtracted from each other to obtain the resultant vector. The resultant magnitude which is computed will be in the same unit as the unit of the input of the vector value. Methods for calculating a Resultant Vector: Interactive simulation the most controversial math riddle ever! We will first resolve each of the forces F1F_1F1 and F2F_2F2 into their respective rectangular components: Similarly, for the force F2F_2F2, we can write: Since the components of a vector are scalar quantities, we can now add them. R = 91 WebThis video explains how to use the parallelogram method to find the resultant sum of two vectors. (, Two forces of magnitude 12.7N and 35N are inclined at an angle of 345, . You can add, subtract, find length, find vector projections, find dot and cross product of two vectors. WebVector Calculator Solve vector operations and functions step-by-step Matrices Vectors full pad FAQ Examples Frequently Asked Questions (FAQ) What are vectors in math? R = A + B = (4i + 3j - 5k) + (8i + 6j - 10k) = 12i + 9j - 15k Answer: Hence the resultant of the two vectors is 12i + 9j - 15k. Vector dimension: Initial point. WebThe resultant vector is the vector that 'results' from adding two or more vectors together. This allows us to allocate future resource and keep these Physics calculators and educational material free for all to use across the globe. Given that there are two forces F 1 = 5N and F 2 = 10N and angle =30o. This calculator performs all vector operations in two and three dimensional space. b divided by the magnitude of vector a |a| times the magnitude of vector b |b| . It is used to determine the direction of the vectors relative to each other. A 2 = P 2 + Q 2 + 2PQCos. You can input only integer numbers, decimals or fractions in this online calculator (-2.4, 5/7, ). create vector equations for each of the given forces. This is obtained by computing the vectors based on the directions with respect to each other. WebResultant Vector Calculator is a free online tool that displays the combination of two or more single vectors. P = Magnitude of the First Vector. There are a two different ways to calculate the resultant vector. WebCalculate the resultant vector of three parallel forces pointing upwards. There are a two different ways to calculate the resultant vector. 1 - Enter the magnitude \( |F_i| \) and the direction of each force.ImportantA) The direction is the angle measured from the positive side of the x axis and is in degrees.B) The magnitudes and directions of the four forces \( \vec {F}_1, \vec {F}_2, \vec {F}_3, \vec {F}_4, \) in the diagram above are used as the default values when you start this page. In order to calculate the magnitude of the vector AB, we need to calculate the distance between the start point A and the endpoint B. Determine if the following set of vectors is linearly independent: $v_1 = (3, -2, 4)$ , $v_2 = (1, -2, 3)$ and $v_3 = (3, 2, -1)$. Then, according to the parallelogram law of vector addition, the diagonal of the parallelogram represents the resultant of vectorsAand B. WebVector calculator. Yes! The formula for calculating the resultant of two vectors is: R = [P 2 + Q 2 + 2PQcos] Where: R = Resultant of the Two Vectors. WebOnline calculator resultant force. its magnitude (its length), which will be force, in Newtons N, and. and to find out the direction, measure the angle of the resultant with the x-axis. The head to tail method to calculate a resultant which involves lining up the head WebConic Sections: Parabola and Focus. The resultant vector formula for the given vectors is given by- r = a + b = (i+2j+3k) + (4i+8j+12k) = 5i+10j+15k The resultant vector from the given vectors is 5i+10j+15k Question 2: Find the resultant vector for the vectors i-2j+5k and 2i-4j+10k Solution: Given two vectors are a=i-2j+5k and b=2i-4j+10k You can input only integer numbers, decimals or fractions in this online calculator (-2.4, 5/7, ). WebResultant Vector Calculator is a free online tool that displays the combination of two or more single vectors. Therefore, with this tool, you can find the magnitude and direction angle of any vector. The angle between two vectors can be found using the dot product formula,: cos() = (A *B) / (||A|| ||B||). WebWhich indicates that the resultant force R has the same direction as a, and has magnitude equal to the product m a.. For example, if a box of 1.5 kg is subject to 5 forces which make it accelerate 2.0 m/s 2 north-west, then the resultant force is directed north-west and has the magnitude equal to 1.5 kg 2.0 m/s 2 = 3.0 N.. Often, however, we know the forces that R = A + B Example 2: Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees. Net Force Calculator. Place the two vectors next to each other such that the head of the one vector is touching the tail of the other vector. The direction ratios of the two vectors are in equal proportion and hence the two vectors are in the same direction. However, the resultant vector vector would be the straight line path from your home to your friend's house, and the black vector represents that path. Consider two vectors A and B acting at a point and represented by the two sides of a parallelogram as shown in the figure. Here A, B are the vectors in the same direction and R is the resultant vector. Sum the square of the horizontal and vertical components of the resultant force and take the square root of the result. The resultant of two vectors can be done in different methods like (1) Using the Triangle Law, (2) Using the Law of Parallelogram, and (3) using Rectangular Components & Pythagoras Theorem. WebAn online calculator to calculate the magnitude and direction of a vector from it components. No units have to be specified when solving for the magnitude. WebThe resultant force calculator finds the magnitude and the direction of the resultant force. How to Use the Resultant Vector Calculator? The subtraction of two vectors A and B can be derived from the formula A - B = A + (-B). seven operations on three-dimensional vectors + steps. WebThis free vector addition calculator allows you to calculate the sum of two vectors (with or without multiples) in a 2d and 3d coordinate system. For each operation, calculator writes a step-by-step, easy to understand explanation on how the work has been done. When many forces act on the same body, the effective motion is determined by the net force: calculate it with ease with CalcTool. Check out 39 similar coordinate geometry calculators . Draw the resultant vector. = 25 + 36 + 60 1/2 Take the square root of the previous result, and this is the magnitude of your two vectors' sum. Find out the resultant vector of the given vectors, Vectors can be added geometrically by drawing them using a common scale according to the. First, we will find the vertical and horizontal components for both forces: F1x=10cos0F_{1x} = 10 \cdot \cos 0 \degreeF1x=10cos0 and F1y=10sin0F_{1y} =10 \cdot \sin 0 \degreeF1y=10sin0. WebThe following resultant vector formula can be used here. WebA vector can be specified either by its magnitude and direction or by its components. You can express or calculate the direction of a vector v in two ways: To calculate the angle \theta that a 2D vector v=(x,y)\vec{v} = (x, y)v=(x,y) forms with the horizontal axis, use this equation: The only problem with this equation is that it doesn't give us the angle about the positive x-axis, but only about the nearest horizontal axis. We know that the effect of a force FFF acting on an object of mass mmm is to accelerate the object according to the equation: Our magnitude of acceleration calculator is a handy tool in case you want to explore more about acceleration. In vector geometry, the resultant vector is defined as: A resultant vector is a combination or, in simpler words, can be defined as the sum of two or more vectors which has its own magnitude and direction.. of each given force, then add the \( x \) components of the forces \( \vec {F}_1, \vec {F}_2, \) to obtain the \( x \) component of \( R_{fx} \) and then add the \( y \) components of the forces \( \vec {F}_1, \vec {F}_2, \) to obtain the \( y \) components of \( R_{fy} \), Components of a Force in a System of Coordinates, Resultant of two Forces - Components, magnitude and direction. WebThe Magnitude of a Vector Formulas: Suppose AB is a vector quantity that has both direction and magnitude. Resultant Force The resultant force due to several forces F 1, F 2, acting on an object is the force R f that has the same physical effects as the different forces acting on that object. You can add, subtract, find length, find vector projections, find dot and cross product of two vectors. Since the cross product is zero we conclude that the vectors are parallel. The head to tail method to calculate a resultant which involves lining up the head Table of Content. \[ |\vec {R}f| = \sqrt { ( R_{fx} )^2 + ( R_{fy} )^2} \] This new vector is defined as the resultant vector. Draw a vector from the beginning of your journey, your home, and the end, your friends house. To best understand how the parallelogram method works, lets examine the two vectors below. Use the head to tail method to calculate the resultant vector in the picture on the right. Finding a resultant vector using components of a vector is known as an analytical method; this method is more mathematical than geometrical and can be regarded as more accurate and precise than the geometrical method, i.e., configuring using the head-to-tail rule. Adding the x-components to find Rx and y-components to calculate RY. Two forces of magnitude 5N and 10N are inclined at an angle of 30o. Thanks for the feedback. Solution WebThe Magnitude of a Vector Formulas: Suppose AB is a vector quantity that has both direction and magnitude. Find out the resultant vector of the following vector parallel to each other, pointing in the same direction, with the positive x-axis, and the second force of 25N is making an angle of 220, with the positive x-axis. Step 3: Finally, the resultant vector will be displayed in the output field. The resultant of two vectors can be done in different methods like (1) Using the Triangle Law, (2) Using the Law of Parallelogram, and (3) using Rectangular Components & Pythagoras Theorem. b divided by the magnitude of vector a |a| times the magnitude of vector b |b| . Q = Magnitude of the Second Vector. The head to tail method to calculate a resultant which involves lining up the head of the one vector with the tail of the other. Let us see how to calculate the net force. Find the cross product of $v_1 = \left(-2, \dfrac{2}{3}, 3 \right)$ and $v_2 = \left(4, 0, -\dfrac{1}{2} \right)$. WebA vector can be specified either by its magnitude and direction or by its components. The head to tail method to calculate a resultant which involves lining up the head of the one vector with the tail of the other. Lets have a better understanding with the help of an example. \[ \theta = \tan^{-1} \left({\frac{R_{fy}}{R_{fx}}}\right) \] with \( \theta \) is in the range \( [0 , 2\pi) \) taking into account the quadrant where the components of the resultant \( \vec {R}f \) are. For a case like this, we use the formula that will square root of the sum of squares of each vector. In math, a vector is an object that has both a magnitude and a direction. Find the angle between the vectors $v_1 = (3, 5, 7)$ and $v_2 = (-3, 4, -2)$. F1x=10\implies F_{1x} = 10 F1x=10 and F1y=0F_{1y} =0F1y=0, F2x=15cos180F_{2x} = 15 \cdot \cos 180 \degreeF2x=15cos180 and F2y=15sin180F_{2y} =15 \cdot \sin 180 \degreeF2y=15sin180. The resultant vector formula is. add the vector equations together to get the vector equation of WebThe consequent vector A is vector Q, which is in the opposite direction of vector P. P Q = A. WebResultant Vector Calculator is a free online tool that displays the combination of two or more single vectors. We can represent these two forces as two vectors F1\overrightarrow{F_1}F1 and F2\overrightarrow{F_2}F2 acting at angles 1\theta_11 and 2\theta_22 (see figure 1). In order to calculate the magnitude of the vector AB, we need to calculate the distance between the start point A and the endpoint B. The two vectors are A = 5 units, B = 6 units and the angle = 60. The directions are measured with respect to the positive x-axis. If several forces are acting together (see figure 2), we can apply the polygon rule and write a more general net force formula as: In the next section, we will see a step-by-step guide to how to find the magnitude and direction of the resultant force? WebCalculator for calculate the coordinates of vector by initial and terminal points. When many forces act on the same body, the effective motion is determined by the net force: calculate it with ease with CalcTool. Example 2: Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees. In order to calculate the magnitude of the vector AB, we need to calculate the distance between the start point A and the endpoint B. WebVector addition and subtraction (V +/- U) The sum of two vectors (V, U) is the vector that results in the sum of the their respective components, such that U + V = (Ux+Vx, Uy+Vy, BYJU'S online resultant vector calculator 409+ PhD Experts 9.7/10 Ratings Vector Calculator. A resultant vector is the result of either the addition, subtraction, multiplication, or division of two or more vectors to yield a new vector. Example 2: Find the resultant of the vectors having magnitudes of 5 units, 6 units, and are inclined to each other at an angle of 60 degrees. Calculate the magnitude of the resultant force. Example 08: Find the cross products of the vectors $ \vec{v_1} = \left(4, 2, -\dfrac{3}{2} \right) $ and $ \vec{v_2} = \left(\dfrac{1}{2}, 0, 2 \right) $. BYJU'S online resultant vector calculator 409+ PhD Experts 9.7/10 Ratings Vector Calculator. It will do conversions and sum up the vectors. You. WebThe procedure to use the resultant vector calculator is as follows: Step 1: Enter the vectors in the respective input field. It will do conversions and sum up the vectors. To find the resultant vector's magnitude, use the pythagorean theorem. If you need help calculating force from Newton's second law of motion, check out the force calculator. v = < v 1 , v 2 >. The resultant magnitude which is computed will be in the same unit as the unit of the input of the vector value. WebThis physics vector calculator will calculate the resultant of two vector quantities, the work done by a force when it moves an object at a certain linear distance, the moment of a force and more Calculator "Excellent Free Online Calculators for Personal and Business use." The books vs. e-books calculator answers the question: how ecological is your e-book reader? Then it changes its course in a direction 165. towards the north. Calculate the magnitude of the resultant force. OA = 5N, OB = 10N and OC = 15N. To find the resultant force or net force acting on an object, follow the given instructions: Determine the horizontal and vertical components of all the individual forces by using the formula: Horizontal component F = F cos Vertical component F = F sin WebThe following resultant vector formula can be used here. How can we deal with this? There angle\:\begin{pmatrix}2&-4&-1\end{pmatrix},\:\begin{pmatrix}0&5&2\end{pmatrix}, angle\:\begin{pmatrix}0&0&a\end{pmatrix},\:\begin{pmatrix}0&1&b\end{pmatrix}. WebThe resultant force calculator finds the magnitude and the direction of the resultant force. In fact, this method of using rectangular What Is A Vector? The resultant R can be determined accurately by drawing a properly scaled and accurate vector addition diagram is shown in the figure below: Let us have a better understanding of the concept with the help of an example. In the XY plane, let A coordinate (a_x^0, b_y^0) and B coordinate (a_x^1 and b_x^1). This week, we will go into some of the heavier \begin{pmatrix}1&0&3\end{pmatrix}+\begin{pmatrix}-1&4&2\end{pmatrix}, (-3)\cdot \begin{pmatrix}1&5&0\end{pmatrix}, \begin{pmatrix}1&2&3\end{pmatrix}\times\begin{pmatrix}1&5&7\end{pmatrix}, angle\:\begin{pmatrix}2&-4&-1\end{pmatrix},\:\begin{pmatrix}0&5&2\end{pmatrix}, projection\:\begin{pmatrix}1&2\end{pmatrix},\:\begin{pmatrix}3&-8\end{pmatrix}, scalar\:projection\:\begin{pmatrix}1&2\end{pmatrix},\:\begin{pmatrix}3&-8\end{pmatrix}. What is a vector angle? Resultant Vector Calculator is a free online tool that displays the combination of two or more single vectors. = 61 + 30 Using the triangle law of vector addition, we know that if two vectors acting simultaneously on a body can be represented in magnitude and direction by the two sides of a triangle taken in one order, the resultant of these two vectors can be represented in magnitude and direction by the third side of the triangle taken in the opposite order (see the net force diagram in figure 1). Solved example: Draw the resultant vector. The three resultant vector formulas are: R = A + B. R = A - B. R2 = A2 + B2 + 2ABCos . We can extend this reasoning to the other cases and come up with the following equations to calculate the direction of the vector in each quadrant: The term arctan(yx)\arctan(\frac{y}{x})arctan(xy) gives an angle in radians, and you must convert it to degrees before using it in the second, third, or fourth quadrant equations. R = A + B = (4i + 3j - 5k) + (8i + 6j - 10k) = 12i + 9j - 15k Answer: Hence the resultant of the two vectors is 12i + 9j - 15k. Multiple vectors may be added together to produce a resultant vector. Solution As we know that the resultant vector is given as: R = OA + OB +OC R = 5 + 10 + 15 R = 30N Example 2 Find out the resultant vector of the given vectors OA= (3,4) and OB= (5,7). Among these three methods, the third one is quite handy to solve vector numerical problems. In math, a vector is an object that has both a magnitude and a direction. Now, putting the values in eq 1.1 to calculate the magnitude of the resultant vector, So, the magnitude of the resultant vector, Two forces of magnitude 5N and 10N are inclined at an angle of 30. . What Is A Vector? Example 1: Find the resultant of the vectors 4i + 3j -5k and 8i + 6j - 10k. If you want to calculate the direction of a vector, you're in the right place. R2 = 91 4.6/5 Star Rating Sum the square of each of the components of the resultant vector. = (, , ) Terminal point. Conic Sections: Ellipse with Foci Continue reading this article to know what net force is and how to find the net force on an object. Vector dimension: Initial point. = (, , ) AB. WebTo calculate the magnitude of a 3D vector, a user enters in all 3 form fields, the vector's x, y, and z values. The interaction of several force vectors on a body is an example of the resultant vector, and the resulting vector is obtained using this formula. There are a two different ways to calculate the resultant vector. Learn about Vectors and Dot Products. Vectors are a powerful tool to represent many physical quantities in our physical world. The rules for finding the resultant of a vector or adding more than two vectors can be protracted to any number of vectors. WebCalculator for calculate the coordinates of vector by initial and terminal points. For each operation, calculator writes a step-by-step, easy to understand explanation on how the work has been done. Suppose there are three vectors in a plane, vector, can be calculated by adding all three vectors. The use of a frame of reference allows us to describe the location of a point in space in relation to other points. || v || = (v 1 2 + v 2 2 ) and the direction of vector v is angle in standard position such that. For each operation, calculator writes a step-by-step, easy to understand explanation on how the work has been done. The head to tail method considers the head of a vector to be the end with the arrow, or the 'pointy end'. The resultant vector is the vector that 'results' from adding two or more vectors together. The resultant vector can be obtained by the following formula. OA = 5N, OB = 10N and OC = 15N. A is indeed the resultant vector, and P and Q are slanted at an angle to each other here. A vector angle is the angle between two vectors in a plane. The resultant vector is the vector that results from adding two or more vectors together. Vector dimension: Initial point. Online Resultant Vector Calculator helps 896+ Math Tutors. Calculate the magnitude and direction of the resultant vector using parallelogram law. As we know that the resultant vector is given as: Find out the resultant vector of the given vectors OA= (3,4) and OB= (5,7). Now join the second vectors tail with the head of the first vector drawn according to the given scale and in the defined direction. Q = Magnitude of the Second Vector. F1x=15\implies F_{1x} = -15 F1x=15 and F1y=0F_{1y} =0F1y=0. Vectors can be added geometrically by drawing them using a common scale according to the head-to-tail convention, which is defined as, Join the tail of the first vector with the head of the second vector, which will give another vector whose head is joined with the head of the second vector and tail of the first vector. As the vertical components, F1yF_{1y}F1y and F2yF_{2y}F2y are zero, the vertical component of the resultant force will be zero. In the picture on the left, the black vector is the resultant of the two red vectors. WebThe following resultant vector formula can be used here. Search our database of more than 200 calculators, Check if $ v_1 $ and $ v_2 $ are linearly dependent, Check if $ v_1 $, $ v_2 $ and $ v_3 $ are linearly dependent. There are a two different ways to calculate the resultant vector. For a case like this, we use the formula that will square root of the sum of squares of each vector. WebThe procedure to use the resultant vector calculator is as follows: Step 1: Enter the vectors in the respective input field. Vectors are a powerful tool to represent many physical quantities in our physical world. Circle skirt calculator makes sewing circle skirts a breeze. More in-depth information read at these rules. The use of a frame of reference allows us to describe the location of a point in space in relation to other points. (, Steps To Find Out The Resultant Vector Using Head-To-Tail Rule, Resultant Vector Of More Than Two Vectors, Calculating Resultant Vector Using Rectangular Components, Finding Resultant Vector Using Parallelogram Method, Resultant vector Explanation and Examples. Unfortunately, in the last year, adblock has now begun disabling almost all images from loading on our site, which has lead to mathwarehouse becoming unusable for adlbock users. To find the magnitude and angle of a resultant force, we. Suppose you want to find the direction angle \theta of the vector Q=(2,4)Q = (-2, 4)Q=(2,4) of the previous image.