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: 50


All vectors in the form of \begin{bmatrix} x \\ -3x \\ \end{bmatrix} $x \in \mathbb{R}$

Work Step by Step

We know that two vectors are orthogonal if their dot product is $0$. Hence: $u\cdot v=0\\x\cdot3+y\cdot1=0\\3x+y=0\\y=-3x$ So all vectors in the form of \begin{bmatrix} x \\ -3x \\ \end{bmatrix} where $x \in \mathbb{R}$ will be orthogonal to $u$
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