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: 39

Answer

$-2x+y=0$
1577027001

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, ${\bf v}=-1\cdot{\bf i} + (-2)\cdot{\bf j}$, $a=-1,\quad b=-2,$ and the lines are $-2x+y=c.$ $P(1,2)$ is on the line $\Rightarrow \left\{\begin{array}{l} -2(1)+(2)=c\\ c=0 \end{array}\right.$ so the line equation is $\quad -2x+y=0$ (a second point on the line is $(0,0)$ )
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