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 30: 49


$k=-2$ or $k=3$

Work Step by Step

We know that two vectors are orthogonal if their dot product is $0$. Hence: $u\cdot v=1\cdot k^2-1\cdot k+2\cdot(-3)=0\\k^2-k-6=0\\(k+2)(k-3)=0$ Thus: $k=-2$ or $k=3$
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