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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?

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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About Math basics & 2D Transformations

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?
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?
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