5) Let A = (4, 1,2) and B= (1,2,-1). Find: a) ProjAB ProjBA b) all nonzero vectors X in R³ orthogonal to A and B c) angle between A and B (measured in degrees)

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

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Q: B) Determine if the two vectors are orthogonal or parallel or not? A=6i + 6k and B--2i +2j+2k

A: We have to check that the two vectors A→ and B→ are orthogonal or parallel. So, we find the angle…

Q: 6. Let a = (1, 0,3) and u = (2,-1,5). a.) (5 pts.) Evaluate projau. b.) (5 pts.) Find a vector that…

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Q: Let 2 = (-8,1) and To (-7, -2) Compute the following vector B Prijz To projections.

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Q: 2 Let a = -1 | and b = 1 | be two vectors 1 What is |al2|b|2 |a · b[? ?

A: Let us consider the vector v=x1,x2,....,xn then the magnitude of the vector is obtained as…

Q: r(t) = (x(t), y(t), z(t)) where x(t) = – 4t2 – 5t – 3 y(t) = 5t² + 5t +3 z(t) = – 5t? - | '(t) =…

A: Here, we need to find the binormal vector B. We are given that r(t)=<x(t), y(t), z(t)> where…

Q: List five vectors in Span {V₁, V₂}. Do not make a sketch. V₁ 9 4, V₂ = -7 4 3 0

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Q: Find the angle between vectors a= (-/2, 0, v2) and b = (-1,1,0). %3D

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Q: Q1: suppose the middle of each side of the triangle is a vector from the vertex (1,2,3), (3,2,1),…

A: Vectors

Q: find the diJ tance betueen the vectors

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Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: Find the angle between the vectors and .

A: Given vectors a=-2i-j+3k b=2i+j-3k

Q: What conditions on a column vector u will make ulu zero? T

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Q: -5 -71 -2 -4 -8 -3 -9 [-1 [3 -2] t A = v = |1 w = -1 and x = 1 -3 5 1 4 v in N(A)? Type "yes" or…

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Q: List five vectors in Span{V₁, V₂}. Do not make a sketch. 6 40-0 V₁ = 3. V₂ = 3 8 6 List five vectors…

A: The given vectors v1=63-8, v2=-630. We have to find five vectors in the Spanv1, v2.

Q: Find the unit vector Â, B, the dot product À. B, and state whether these 2 vectors are orthogonal,…

A: Given vectors are- A→=3,-2 and B→=2,4 To find the unit vector A^, B^ and dot product A.B Unit vector…

Q: For any vector v = (a, b, 0), where a and b are any nonzero real numbers, Select one: True False vok…

A: Here I have written the notion, I have used in my solution

Q: 3) |x| = 7, y = 8, and|x - y = 10, determine | x + y. Hint: sketch out these 4 vectors on the same…

A: We know that the vector parallelogram rules  ||A+B||^2+||A-B||^2=2||A||^2+2||B||^2

Q: 4) Consider the vectors u = [3, -2] and v= [-5, 4], write a = [-24,18] as a linear combination of u…

A: The given vectors  and .The objective is to write the vector  as a linear combination of  and .

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: Write the vector v= 1 as the linear combination of vectors --0 w =

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