H [3t-2] t+3 [2t-3] (a) Find all values of t for which w and z are orthogonal. 2. Consider the vectors w= and z= (b) Compute the projection of the vector z onto w; your answer should be a vector whose components are expressions in terms of t. (c) Find a point P in R³ such that the points (0,0,0), (1,-1, 1), (4, 5, 1), and P form a rectangle. Explain your reasoning.
H [3t-2] t+3 [2t-3] (a) Find all values of t for which w and z are orthogonal. 2. Consider the vectors w= and z= (b) Compute the projection of the vector z onto w; your answer should be a vector whose components are expressions in terms of t. (c) Find a point P in R³ such that the points (0,0,0), (1,-1, 1), (4, 5, 1), and P form a rectangle. Explain your reasoning.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 13CR
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Question
![2. Consider the vectors w =
B
and z=
[3t-2]
t +3
2t-3
(a) Find all values of t for which w and z are orthogonal.
(b) Compute the projection of the vector z onto w; your answer should be a vector
whose components are expressions in terms of t.
(c) Find a point P in R³ such that the points (0, 0, 0), (1,-1, 1), (4,5, 1), and P form
a rectangle. Explain your reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c36485c-0099-4862-8f3c-a0eecaf9cef9%2Fa1062b2e-a6b7-47ae-b877-850b2f516361%2Fgcjmxw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the vectors w =
B
and z=
[3t-2]
t +3
2t-3
(a) Find all values of t for which w and z are orthogonal.
(b) Compute the projection of the vector z onto w; your answer should be a vector
whose components are expressions in terms of t.
(c) Find a point P in R³ such that the points (0, 0, 0), (1,-1, 1), (4,5, 1), and P form
a rectangle. Explain your reasoning.
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