Chapter 8.4, Problem 18E

To determine

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

Answer to Problem 18E

Inner product is 0.

Yes

Explanation of Solution

Given information:

  $\langle -2,4,8\rangle \cdot \langle 16,4,2\rangle$

Calculation:

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

  $\begin{array}{c}\langle -2,4,8\rangle \cdot \langle 16,4,2\rangle =\left(-2\right)\left(16\right)\text{+}\left(4\right)\left(4\right)\text{+}\left(8\right)\left(2\right)\left[\text{Using }\overrightarrow{a}\cdot \overrightarrow{b}=a_1{b}_1+a_2{b}_2+a_3{b}_3\right]\\ =-32+16+16\\ =0\end{array}$

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.