Chapter 9.2, Problem 15E

To determine

The perpendicularity of the given vector.

Answer to Problem 15E

The given vector is perpendicular.

Explanation of Solution

Given :

  $\begin{array}{l}\text{u = }\langle 6,4\rangle \\ \text{v = }\langle -2,3\rangle \end{array}$

Calculation:

Definition of perpendicularity: Two vectors are said to be perpendicular if there dot product is zero;

i.e., $\text{u}\text{.v}=0$ .

Now,

  $\begin{array}{l}\text{u =}\langle {\text{a}}_{\text{1}}{\text{,b}}_{\text{1}}\rangle \text{and}\text{v =}\langle {\text{a}}_{\text{2}}{\text{,b}}_{\text{2}}\rangle \\ \text{u}{\text{.v = a}}_1{\text{a}}_2+{\text{b}}_{\text{1}}{\text{b}}_{\text{2}}\end{array}$

So,

  $\begin{array}{l}\text{u}\text{.v = }\left(6\right)\left(-2\right)+\left(4\right)\left(-3\right)\\ \text{u}\text{.v = }-12+\left(-12\right)\\ \text{u}\text{.v}=0\end{array}$

Therefore; the given vectors are perpendicular.