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Q - Answer the following questions with brief justifications. Find two vectors u and v such that u × v = = (0,6, 0). The answer is not unique. b) Give an example of a vector a such that proj₁ (2, 3, 4) = 2a. The answer is not unique. C) Does there exist a vector v such that (1, 2, 1) × v = (3,1,5)? If yes, find an example. If not, explain why.

Q - Answer the following questions with brief justifications. Find two vectors u and v such that u × v = = (0,6, 0). The answer is not unique. b) Give an example of a vector a such that proj₁ (2, 3, 4) = 2a. The answer is not unique. C) Does there exist a vector v such that (1, 2, 1) × v = (3,1,5)? If yes, find an example. If not, explain why.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 52EQ
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Q - Answer the following questions with brief justifications. o) Find two vectors u and v such that u × v = (0,6, 0). The answer is not unique. b) Give an example of a vector a such that proj, (2, 3, 4) = 2a. The answer is not unique. C) Does there exist a vector v such that (1, 2, 1) x v = (3, 1,5)? If yes, find an example. If not, explain why.
Transcribed Image Text:Q - Answer the following questions with brief justifications. o) Find two vectors u and v such that u × v = (0,6, 0). The answer is not unique. b) Give an example of a vector a such that proj, (2, 3, 4) = 2a. The answer is not unique. C) Does there exist a vector v such that (1, 2, 1) x v = (3, 1,5)? If yes, find an example. If not, explain why.
(a) u = 2k = (0, 0, 2), v = 3î = (3, 0, 0). (b) a=i= (1,0,0). - (c) (1, 2, 1) × v should be orthogonal to both (1, 2, 1) and v. However, (3, 1, 5) is not orthogonal to (1, 2, 1). So no such v exists.
Transcribed Image Text:(a) u = 2k = (0, 0, 2), v = 3î = (3, 0, 0). (b) a=i= (1,0,0). - (c) (1, 2, 1) × v should be orthogonal to both (1, 2, 1) and v. However, (3, 1, 5) is not orthogonal to (1, 2, 1). So no such v exists.
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