(13) Find the cosine of the angle between the given vectors. (13a) (3, 1, 1) and (2, –4, 2) (13b) i + j and j + 2k (14) Let v = (2,3/2, –3) and w = (-4, –3, 6). Show that v and w are parallel. (15) Let v = (4, 1, –5) and w = (9, 4, 8). Show that v and w are perpindicular.

Q: Consider the following vectors. u (6, –5) and v = (9, 1) u + v = (12, – 3) | (c) Find 7v – u. 7v – u…

A: By algebra of vectors we solve the this question.

Q: Given r = (5, 2, 3) and s = (-4, -2, 2) and t = (3, 4, 1) %3D a. Write the unit vector for S b.…

A: This question can be solved using the concept of unit vector and linear combination of vectors.

Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

A:

Q: 9. Find the dot product of the following pairs of vectors. a. u= (1, 3), v = (5,-2) b. = (9,-4), v =…

A:

Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

A:

Q: 3. Determine which of the pairs of vectors are orthogonal. (a) a = (b) u = (c) y = 8 12 -5 3,0 = -3…

A:

Q: 1. 2. 3. Find a vector equation of line passing (1,-1,4) in the direction of (3,5,-2). Find a vector…

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Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

A:

Q: Let = [-3 1] and = [1 2]. Find the following vectors. [ ]]. ]]. u = 7y= = [1 w = 2x + 7y = [ v=27=…

A: Given: Let x→=[-3  1] and y→=[1  2].

Q: Consider the following points. A(3, 1, 1), B(4, -4, 6), C(7, -2, 0), D(6, 3, −5) Let u = AB, VAC,…

A: Consider the following points.Let , , and . Find each of these vectors.Find the scalar triple…

Q: For the given vectors u and v, find the proj,u and proj,v. 1. u = (10, 5) and v (2, 6). V =

A: Question- For the given vectors u and v, calculate projvu and scalvu. u = ⟨10, 5⟩ and v = ⟨2, 6⟩

Q: Let P = (3, –2), Q = (1,4), R= (-2,5), S= (-4,6) Find the component and linear %3D combination form…

A: We have to find vectors

Q: p (x )EP 2 (R ), p (x ) = 3x? +x - 5 of the vector {1,x 1,x +1} Based on base Which of the following…

A: Given:  p(x) = 3x2+x-5

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: 0 Let a = -(1)-(3) 0 What is a|2|b²+ a. b² ? and b= 2 be two vectors.

A:

Q: Let i = [1 -4] and y = [4 -6]. Find the following vectors. i = 57 ü = 2g =| w = 5i + 2j =||

A: The solution is given below:-

Q: Place the vectors a, b, c, and d in order of length, from smallest to largest. Show your…

A: We have to find length of each vectors first.

Q: For the vectors u = 3ỉ − 8j + 2k and - v = 4i - 2j – 4k we have - ü × v = 28i + 20j +38k. Select…

A: The given vectors

Q: (a) Let w =(-5,-17,7), v 1=(0,-1,1), v² 2=(0,-2,1), v 3=(1,2,-1). If possible, express w as a linear…

A:

Q: For the vectors u (1,0, 1) and v (0, 2, 1), u x v = %3D O A. (1, 2, 0) O B. (1, 2, -2) OC. (2, 1, 2)…

A: Given. The vectors u = 1, 0, 1 v = 0, 2, 1 We have to find u×v