Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y|| ≤ 1, prove that √1- ||1||² √/1 − ||y||² ≤ 1 − |x · y|. /1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 55E
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1. Let z, y € R" be given.
(a) If ||z|| = ||y|| = 1 and z-y = 1, show that x = y.
(b) If ||z|| ≤ 1 and ||y|| ≤ 1, prove that √√1 - ||1||²√√/1 – ||y||² ≤1 − |z · y|.
Transcribed Image Text:1. Let z, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that x = y. (b) If ||z|| ≤ 1 and ||y|| ≤ 1, prove that √√1 - ||1||²√√/1 – ||y||² ≤1 − |z · y|.
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