Find the angle between the vectors v and w in each of the following: (a) v = (2, 1, 3)", w = (6, 3, 9)" (b) v = (2, –3)",w = (3, 2)" (c) v = (4, 1)", w = (3, 2)" (d) v = (-2, 3, 1)", w = (1, 2, 4)" For each pair of vectors in Exercise 1, find the scalar projection of v onto w. Also, find the vec- tor projection of v onto w.

Q: Graph and find the area of the parallelogram formed by the vectors u = and v = .

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Q: (e) Find the angle between two vectors u = (4, -3, 6) and v = (3, 0, 1).

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Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: 5. For the vectors = (-3, –4) and v = (-2, 2) Find the dot product u · v, and the angle 0 between…

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Q: 1. Add the following three vectors to find the resultant vector, R: šj = (-2,0)m, .ž= (0,–5,)m, .řz…

A: 1.   x1¯  =  (-2,0)mx2¯  =  ( 0, -5)mx3¯   =  (3,0)m Now , In the East - west direction ,  we deal…

Q: Sketch 2v, -w, v+w, and 2v-w for the vectors in Figure 24. 5 y 4 3 v = (2,3) 2 1 w = (4, 1)

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Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: 2. For v = (5,-2) and w = (3, 4), find v+w, v - w, v/2, -w and make one sketch labeling all 6 of…

A: Given,           v=<5,-2> and w=<3,4>

Q: 5. For vectors given the vectors v =(-4,-3) and w (-1,-1), find: (a) Sketch, v+w below. Find its…

A: We can solve as follows

Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

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Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

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Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

A: If we have a vector u=a,b,c, then the unit vector that is in the direction of vector u is the vector…

Q: 5. Let A = (4,3), B = (0, 1), and C = (−3, 7). (a) Find the vectors AB, BC, and AT. (b) Prove that…

A: Step 1:It is provided that, A=(4,3),B=(0,1), and C=(−3,7). (a) Then, it is obtained:AB=B−A…

Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

Q: Find two different combinations of the three vectors u = (1,3) and v = (2,7) and w = (1,5) that…

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Q: For parts (a)-(e), please use the following vectors: C = (-1,-1,0) -120°, and 0₂ = 90° A = (2,4,0) B…

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