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: 33

Answer

$x+2y=4$
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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, ${\bf v}=1\cdot{\bf i} + 2\cdot{\bf j}$, and the lines are $x+2y=c.$ P(2,1) is on the line $\Rightarrow \left\{\begin{array}{l} (2)+2(1)=c\\ c=4 \end{array}\right.$ so the line equation is $\quad x+2y=$4 (intercepts: $(4,0)$ and $(0.2)$ )
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