2. Let a, b and c be vectors in R". Prove that(a) a and (ac)b (a b)c are perpendicular;|a - b|²a|²b|2ab(b) if a, b are nonzero vectors, then||a|2 |b|2(c) |a+b = |ab| if and only if a and b are perpendicular.

Answered: Image /qna-images/answer/66ff7bb6-01c5-489b-bff6-fc158da08659.jpg

2. Let a, b and c be vectors in R". Prove that (a) a and (a c)b - (a - b)c are perpendicular; a b (b) if a, b are nonzero vectors, then ||a|2 b2 (c) |a+b| = |ab| if and only if a and b are perpendicular. |a - b|² a/²/b/2;

2. Let a, b and c be vectors in R". Prove that (a) a and (a c)b - (a - b)c are perpendicular; a b (b) if a, b are nonzero vectors, then ||a|2 b2 (c) |a+b| = |ab| if and only if a and b are perpendicular. |a - b|² a/²/b/2;

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 22E

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Question

2. Let a, b and c be vectors in R". Prove that
(a) a and (ac)b (a b)c are perpendicular;
|a - b|²
a|²b|2
a
b
(b) if a, b are nonzero vectors, then
||a|2 |b|2
(c) |a+b = |ab| if and only if a and b are perpendicular.

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