Chapter 8.4, Problem 7MCQ

To determine

To find: the inner product of the vectors and state whether they are perpendicular by writing yes or no.

Answer to Problem 7MCQ

Inner product is 0.

Yes

Explanation of Solution

Given information:

  $\langle 3,6\rangle \cdot \langle -4,2\rangle$

Calculation:

The inner product of the vector can be evaluated as follows:

  $\begin{array}{c}\langle 3,6\rangle \cdot \langle -4,2\rangle =\left(3\right)\left(-4\right)\text{+}\left(6\right)\left(2\right)\left[\text{Using }\overrightarrow{a}\cdot \overrightarrow{b}=a_1{b}_1+a_2{b}_2\right]\\ =-12+12\\ =0\end{array}$

Thus the inner product of the vector is 0.

Since the inner product of the vector is zero, so the vectors are perpendicular to each other.