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Two vectors in the plane, i & j, have the following properties: i · i = 1, i • j = 0, j • j = 1 a) Is there a vector k, that is not equal to i, such that: k·k = 1, k. j = 0? What is it? Are there many vectors with these properties? b) Is there a vector k such that: k k = 1, k.j = 0, ki = 0? Why not? c) If i and j were vectors in 3D, how would the answers to the above questions change?

Two vectors in the plane, i & j, have the following properties: i · i = 1, i • j = 0, j • j = 1 a) Is there a vector k, that is not equal to i, such that: k·k = 1, k. j = 0? What is it? Are there many vectors with these properties? b) Is there a vector k such that: k k = 1, k.j = 0, ki = 0? Why not? c) If i and j were vectors in 3D, how would the answers to the above questions change?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.CR: Chapter Review
Problem 8CC
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Two vectors in the plane, i & j, have the following properties: i · i = 1, i · j = 0, j · j = 1
a) Is there a vector k, that is not equal to i, such that: k · k = 1, k · j = 0? What is it? 
Are there many vectors with these properties?
b) Is there a vector k such that: k · k = 1, k · j = 0, k · i = 0? Why not?
c) If i and j were vectors in 3D, how would the answers to the above questions 
change?

Two vectors in the plane, i & j, have the following properties: i ·i = 1, i·j = 0,j ·j = 1 a) Is there a vector k, that is not equal to i, such that: k k = 1, k·j = 0? What is it? Are there many vectors with these properties? b) Is there a vector k such that: k·k = 1, k · j = 0, k · i = 0? Why not? c) If i and j were vectors in 3D, how would the answers to the above questions change? %3D
Transcribed Image Text:Two vectors in the plane, i & j, have the following properties: i ·i = 1, i·j = 0,j ·j = 1 a) Is there a vector k, that is not equal to i, such that: k k = 1, k·j = 0? What is it? Are there many vectors with these properties? b) Is there a vector k such that: k·k = 1, k · j = 0, k · i = 0? Why not? c) If i and j were vectors in 3D, how would the answers to the above questions change? %3D
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