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: 38

Answer

$3x-2y=4$
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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, ${\bf v}=2\cdot{\bf i} + 3\cdot{\bf j}$, $a=3,\quad b=3,$ and the lines are $3x-2y=c.$ $P(0,-2)$ is on the line $\Rightarrow \left\{\begin{array}{l} 3(0)-2(-2)=c\\ c=4 \end{array}\right.$ so the line equation is $\quad 3x-2y=4$ (a second point on the line is $(2,1)$ )
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