# Chapter 12: Vectors and the Geometry of Space - Section 12.3 - The Dot Product - Exercises 12.3 - Page 713: 36

$2x-3y=-8$

#### 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, ${\bf v}=2\cdot{\bf i} + (-3)\cdot{\bf j}$, and the lines are $2x-3y=c.$ $P(11,10)$ is on the line $\Rightarrow \left\{\begin{array}{l} 2(11)-3(10)=c\\ c=-8 \end{array}\right.$ so the line equation is $\quad 2x-3y=-8$ (a second point on the line is $(-4,0)$ )

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