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: 51

Answer

$c\left[ \begin{array}{ c c } b \\ -{a} \end{array} \right]$

Work Step by Step

Given u=(x,y),v=(a,b) vector u and v are orthogonal if there dot product is zero. $u.v=0$ $x\cdot a+y \cdot b=0$ $ax+by=0$ $y=-\frac{ax}{b}$ So the vector orthogonal to u is: $ \left[ \begin{array}{ c c } x \\ -\frac{a}{b}x \end{array} \right]=\frac{x}{b}\left[ \begin{array}{ c c } b \\ -{a} \end{array} \right]=c\left[ \begin{array}{ c c } b \\ -{a} \end{array} \right]$
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