2. Find vectors v, w E R³ such that v + w = (1,3,7), v is parallel to (1, 0, 1), and w is orthogonal to (1, 0, 1).

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: 1. y -2+ 2.

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Q: 1 u=-----(1, 1, 1, 0), V 3 1 -- (-1,-1, 2, 0) W = V6 1 =(1,-1, 0, 0) V 2

A: Here we have to determine whether or not the following set of vectors { u, v, w } are both…

Q: Let ā= −i − 2j + 3k, b = i - 2j + 3k, c = −i +2j - 3k.

A: The given vectors .The objective is to find the vector that is perpendicular to both  and .

Q: Let =(5,4,1),(3,-4, 1), w=(1, -2, 3). Which pair of vectors, if any, are perpendicular (orthogonal)?…

A: We have to find out solution

Q: u = (2, 3,-1) v= (0, 1, -2) w = (2, 4, -3).

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Q: 3. Given two vectors x = [0, 1, 1] and y = [- 3, 0, 0], use your knowledge of vectors to determine…

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Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

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 non parallel and two parallel vectors both orthogonal to (1, 2, 3)

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Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V1, V2, V3) such…

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Q: = 2. Are the vectors V = (2, — 4, 1) and w Show work and briefly explain. (3, 2, 2) orthogonal? 3.…

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Q: Consider the vectors u =(1,9,4) and v =(-16,0,-4).| The vector W" =(x,0,z) that simultaneously…

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Q: 5. Consider a unit vector u = (a,b). (a) How many unit vectors are orthogonal to u? (b) Explain a…

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Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

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Q: Determine which of the vectors is parallel to z and which is orthogonal to z if z = (3, 2) Show work…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

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Q: 1) Given ū = (3, -5) and v = (1, 3), calculate proj,ū . 2) Given the vectors ū =i +2j+3k and = 2i –…

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Q: Let u = (2, 1, -2), v= (0,3,-5), and w = Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) -…

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Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

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Q: b) u = (3, -1), v = (1, 5) et w = (8, -2) c) i = (1, 0, 0), j = (0, 1, 0) et k = (0, 0, 1) gajte…

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Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…