Chapter 13.4, Problem 19WE

To determine

To find: The value of k.

Answer to Problem 19WE

The value ofkis $-12$ .

Explanation of Solution

Given information: The vectors $\left(8,k\right)$ and $\left(9,6\right)$ are perpendicular.

Concept used: If the product ofthe slopes of two vectors are $-1$ , then the vectors are perpendicular.

Calculation:

Slope of $\left(8,k\right)$ is $\frac{k}{8}$ .

And slope of $\left(9,6\right)$ is $\frac{6}{9}$ .

If the product of the slopes of two vectors are $-1$ , then the vectors are perpendicular.

So,

  $\begin{array}{l}\frac{k}{8}\times \frac{6}{9}=-1\\ k=-12\end{array}$