Let a e R" be fixed. Suppose that vectors x, y e R" are related by the equation а — х+ (х-у)у. a) Show that |a||2 – ||x||? 2+ ||y||? (х-у)? %3D b) Deduce that ||a|| > ||x||-

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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Let a e R" be fixed. Suppose that vectors x, y e R" are related by the equation
a=x+(x·y)y.
a) Show that
|a||2 – ||x||?
2+ ||y||?
(x. y)?
%3D
b) Deduce that ||a|| > ||x||-
Transcribed Image Text:Let a e R" be fixed. Suppose that vectors x, y e R" are related by the equation a=x+(x·y)y. a) Show that |a||2 – ||x||? 2+ ||y||? (x. y)? %3D b) Deduce that ||a|| > ||x||-
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