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1. Prove that if u and v are vectors in Rn, then |u·v| s ||u|||v|| where ju v| denotes the absolute value of u · v.

1. Prove that if u and v are vectors in Rn, then |u·v| s ||u|||v|| where ju v| denotes the absolute value of u · v.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 19E
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1. Prove that if u and v are vectors in Rn, then |u·v| < ||u|||v|| where ju v| denotes the absolute value of u· v. 2. Show that the function (p,q)=a,bo+a¡b1+ażb2 in P2 defines an inner product for polynomials p(x)= ao+a1x+a2x² and q(x)= bo + b,x + b2x².
Transcribed Image Text:1. Prove that if u and v are vectors in Rn, then |u·v| < ||u|||v|| where ju v| denotes the absolute value of u· v. 2. Show that the function (p,q)=a,bo+a¡b1+ażb2 in P2 defines an inner product for polynomials p(x)= ao+a1x+a2x² and q(x)= bo + b,x + b2x².
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