Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.3 - The Dot Product - Exercises 12.3 - Page 713: 37

Answer

$-x-y=1$
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Work Step by Step

The result of exercise 32 tells us that ${\bf v}=a{\bf i} + b{\bf j}$ is parallel to the lines $bx-ay=c$ Here, ${\bf v}=1\cdot{\bf i} + (-1)\cdot{\bf j}$, $a=1,\quad b=-1,$ and the lines are $-x-y=c.$ $P(-2,1)$ is on the line $\Rightarrow \left\{\begin{array}{l} -(-2)-(1)=c\\ c=1 \end{array}\right.$ so the line equation is $\quad -x-y=1$ (a second point on the line is $(-1,0)$ )
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