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: 35

Answer

$-2x+y=-3$
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Work Step by Step

The result of exercise 31 tells us that ${\bf v}=a{\bf i} + b{\bf j}$ is perpendicular to the lines $ax+by=c$ Here, ${\bf v}=-2\cdot{\bf i} + 1\cdot{\bf j}$, and the lines are $-2x+y=c.$ $P(-2,-7)$ is on the line $\Rightarrow \left\{\begin{array}{l} -2(-2)+(-7)=c\\ c=-3 \end{array}\right.$ so the line equation is $\quad -2x+y=-3$ (a second point on the line is $(0.-3)$ )
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