: (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit vectors U, and U2 perpendicular to u, and u2.

Q: You deposit $100 each month into an account earning 6.3% interest compounded monthly for 30 years.…

A: Here given  Principle amount P=$100 rate r=6.3% time t=30 years,

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

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Q: Suppose A is a 2 by 3 matrix. Does Ax = 0 always have infinitely many solutions? Give a reason. Does…

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Q: Vector A is 35 m long and makes an angle of 60° clockwise from the positive Y-axis. Vector B is 55m…

A: We have given a vector A of magnitude 35 m and makes angle 60∘ from the positive y-axis i.e. 30∘…

Q: Q1 Given A= 3i-7j+5k, B = -i+7j-k, C = 4i-j+k. Find the unit vector of: (а) А-В+С (b) АхСхВ

A: The vector addition can be performed by the addition of the respective elements. The elements with…

Q: The vector v= (6,-4, 0) starts at the point P = (-2,5, -1). At what point does the vector end?…

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Q: u = (1,2, 0), v = (-1,4, 1)

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Q: Q1/For the figure bellow: a- Write all vectors in vector pair form. i.e. b= (2,1). b- Write all…

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Q: sider the following coordinates and vectors, A(-2, 1, 0), B(2, -2,0), u = 3i + 2k, v = 4i + 7j+5k,…

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Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: Find two unit vectors orthogonal to a = (-2,-1, 3) and b = (5,-2, 1) Enter your answer so that the…

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Q: Given the vectors, ū = -3i+2j and = 4i – j, find 4ü-27. %3D (-20,10) (20,-10) (-20,-10) (20,10)

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Q: Given two vectors P=a,-a, Q-2а, -а, ta, R=2a,+3a,+a, Determine: (a). (P+Q)x(P-Q) (b). Q.RxP (c)…

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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: b) Consider the vectors u = (2c, 2, −4), v=(c, c, 3)and w = (-1, 2, 3). Find the value(s) of…

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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: (d) Let w =(-39,22), v’i=(2–5), v°2=(5,-4), v°3=(-4,-1). If possible, express w as a linear…

A: In this question we need to multiply vectors by constant and have to find values of constant

Q: Determine the angles between the following pairs of vectors. (a) (−1, 1), (0, 1)     (b) (2, 0), (1,…

A: To determine the angles between the following pairs of vectors.

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: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: (1) Let a and b denote two vectors. Try to prove (a x b)² = a²b² – (a · b)² (2) For the triangle…

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Q: mine the angle between vectors M = (1

A: Here we vector M=1,2,5 and vector T=-2,-3,3

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 5v

A: Given that u=-3, 4  and  v=2, -5. This implies that, 5v=5·2, -5=5·2, 5·-5=10, -25 Thus, the…

Q: a = 2î - j+ 3k b=i-sj+2k c = 4j-k (а) (b) (c) (d) Determine the sum of the vectors a, b and c.…

A: Given      a=2i ^-j ^+3k^  b=i^-5j^+2k^c=4j^-k^ We have to find sum of all vector , magnitude , unit…