Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 1 - Vectors - 1.2 Length and Angle: The Dot Product - Exercises 1.2 - Page 290: 18


The angle is an obtuse angle.

Work Step by Step

Given u and v are two vectors: $\cos\theta=\frac{u.v}{|u||v|}$ Thus, we find theta: $u.v=3(-1)+0(1)=-3$ $|u|=\sqrt{(3^2+0)}=3$ $|v|=\sqrt{((-1)^2+1^2)}=\sqrt{2}$ so $\cos\theta=\frac{u.v}{|u||v|}=\frac{-3}{3\sqrt{2}}=\frac{-1}{\sqrt{2}}$ $\theta =135 degree$ This is greater than 90 degrees, so the angle is obtuse.
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