Let u = = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that the angle between u − ||w||²w and v is 30°. -

Q: = (-4, –1,6) and v = (3, –2, 1) and let 0 be the angle between u and v. Then, Let u = OA. 0 = 0. O…

A: in this question, firstly calculate the dot product of vectors and find the angle using formula.

Q: Find u · (v x w). (4, 4, 4) (4, 6, 0) w = (0, 0, 9) u = V =

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Q: 6. V=(2,-3). W=(4, 5) Find (a) 2v-w, ( b) V.W (C) angle between V and W

A: 6. The given data is: V=2,-3, W=4,5 To find the value: a 2V-W

Q: Find the angle between v and w if v · w = 1/2 ||v|| ||w||.

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Q: Given =16,-2,k) and V=14,-4, 0]. Determine the value(s) of k if the angle between ü and v is 60°.

A: We will find the possible values of K as shown below

Q: Let A = –2a, + 5a, + a, B = a, + 3a, and C = 4a, –6a, + 10a.. (a) Determine A – B + C (b) Find A ·…

A: Given vectors: A=-2ax+5ay+az B=ax+3az C=4ax-6ay+10az

Q: Assume that ||v|| = 3, ||w||= 5, and the angle between v and w isθ = π/3 .  Find ||v + w||.

A: Given: v=3,w=5,θ=π3 We know that v+w is given by v+w=v2+w2+2vwcosθ…

Q: Consider the following. u = (2, 0), v = (5, 7) (a) Find u · v. U'V = (b) Find the angle between u…

A: Given that  The vectors  u=(2,0) and v=(5,7) To find the u.v and angle between the u and v

Q: If 0 is a first quadrant angle where P(u, v) = (-1, -2), tan 0: 5 + V5 - V5 5 - 5 - V5 5 + V5 5 - V5…

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Q: Find u · v, where 0 is the angle between u and v. ||u|| = 100, ||v|| = 230, 0 6

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Q: 1. Let u = PQ and v = PR, where P = (2, –1,3), Q = (0,5, 1), and R = (5,5, %3D (a) u v (b) The angle…

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Q: Find a · b if |a| = 14, |b| = 9, and the angle between a and b is 7/2.

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Q: When is OP perpendicular to AB?

A: According to the given figure, A(a, 0), B(0, b) and O(0, 0). We know that slope of a line passes…

Q: Determine whether u and v are orthogonal, parallel, or neither. u = (cos(0), sin(0), 8) v = (sin(0),…

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Q: Let Pi(0,0, 1), P2(1, 1,0) and P3(0, 1, 1) be three points in R®. Evaluate cos LP, P P3, where LP,P…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find u · v, where 0 is the angle between u and v. ||u|| = 4, ||v|| = 14, 0 = - 3

A: This problem can be solved by directly putting given values in the formula for the dot (or scalar)…

Q: Find u · v, where 0 is the angle between u and v. ||u|| = 4, ||v || = 64, 0 4

A: Directly use the formula for dot product of two vector and simplify the result.

Q: Q1 : Find the angle between u = 2i + j- 2k and v = i+j+k.

A: The angle between two vectors: - Consider two vectors a and b that are separated by an angle. Then,…

Q: 1. Find the distance between p(-2, 3,0) and Q(2,1,5). 2. Find the direction of A = 2i - 3j+7k. 3.…

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Q: Find the cosecant (if it exists) of the angle √2 √√2 2 0-√2 O 0-220 √2 0 = 5л 4

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Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3, 2, 4), and w=(-6,1,1). V

A: Angle between two vector V and W found using cosine function

Q: Rotate points P/(1,1,1), P2(2,1,2), P3(2,3,1) & P4(1,3,2) +30° around

A: Here, in the question We have to rotate the points about the points P1(1, 1, 1) , P2( 2, 1, 2),…

Q: Find u - v, where e is the angle between u and v. 27 |매 10, ||v|| = 17, 0 = , |u|| 3

A: Given: u→=10 ,     v→=17  Angle between both vectors is:  θ=2π3

Q: Let v = 2 1 - 3 + 5k, and u = -2 i + 3j - 5k, Calculate vll, ull, Ilv • ūll, and 8 (the angle…

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Q: Let = -2- 4 V u = −2+ 4 Calculate , ul, (the angle between (2 decimal places) lull = + 5 K, and -…

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