Explanation Given: Given that u ≠ 0 , v ≠ 0 such that | | u | | = | | v | | . Approach: Using vector algebra to solve the three space orthogonality, such that u + v be obtained by addition of the vectors u and v , where u − v be obtain by taking difference and orthogonality would be checked by taking the dot product, that is ( u − v ) ⋅ ( u + v ) , as if the dot product is equal to zero then the following vectors are orthogonal. Calculation: Since it is a condition, which states that two vectors are known to be orthogonal if and only if u ⋅ v = 0 Also if u , v are of three space then their dot product denoted by u ⋅ v = u 1 v 1 + u 2 v 2 + u 3 v 3 Such that vector basis u + v = [ u 1 u 2 u 3 ] + [ v 1 v 2 v 3 ] = [ u 1 + v 1 u 2 + v 2 u 3 + v 3 ] u − v = [ u 1 u 2 u 3 ] − [ v 1 v 2 v 3 ] = [ u 1 − v 1 u 2 − v 2 u 3 − v 3 ] Now let’s take scalar dot product of these expressions

Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

5th Edition

ISBN: 9780134689531

Author: Lee Johnson, Dean Riess, Jimmy Arnold

Publisher: PEARSON

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Chapter 2.CE, Problem 12CE

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Let u and v be non-zero vectors such that ||u|| = ||v||, show that u−v and u+v are orthogonal.

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Chapter 2.CE, Problem 11CE

Chapter 3.1, Problem 1E

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Introduction to Linear Algebra (Classic Version) (5th Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 2.1 - In Exercises 1-4, graph the geometric vector u=AB...Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Let u=AB and v=CD where...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - In Exercises 6-9, find the unspecified coordinates...Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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Let u and v be non-zero vectors such that | | u | | = | | v | | , show that u − v and u + v are orthogonal.

Solution Summary: The author explains how vector algebra solves the three-space orthogonality by adding the vectors u and v.

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To show:

Let u and v be non-zero vectors such that ||u|| = ||v||, show that u−v and u+v are orthogonal.

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Chapter 2 Solutions

Let u and v be non-zero vectors such that | | u | | = | | v | | , show that u − v and u + v are orthogonal.

Solution Summary: The author explains how vector algebra solves the three-space orthogonality by adding the vectors u and v.

Videos

To show: Let u and v be non-zero vectors such that ||u|| = ||v||, show that u−v and u+v are orthogonal.

Want to see the full answer?

Chapter 2 Solutions

To show:

Let u and v be non-zero vectors such that ||u|| = ||v||, show that u−v and u+v are orthogonal.