Chapter 11, Problem 9CLT

To determine

To calculate:

The vector parallel, orthogonal or neither:

  $\begin{array}{l}u=\left(4,4,0\right)\\ v=\left(0,-8,6\right)\end{array}$

Answer to Problem 9CLT

The vectors $u=\left(4,4,0\right)$ and $v=\left(0,-8,6\right)$ neither parallel nor orthogonal

Explanation of Solution

Given information:

  $\begin{array}{l}u=\left(4,4,0\right)\\ v=\left(0,-8,6\right)\end{array}$

Calculation:

Know that,

  $\begin{array}{l}u=\left(4,4,0\right)\\ v=\left(0,-8,6\right)\end{array}$

Know that,

The vectors $u$ and $v$ are parallel to each other:

  $u=cv$ .

  $c=$ Constant

Consider the vector $v=\left(0,-8,6\right)$

Therefore, the vectors $u=\left(4,4,0\right)$ and $v=\left(0,-8,6\right)$ are not parallel

Check that vector are orthogonal or not, compute the dot product of $u$ and $v$ . If dot product is zero then it will be orthogonal.

  $\begin{array}{l}u\cdot v=\left(4,4,0\right)\cdot \left(0,-8,6\right)\\ u\cdot v=4\left(0\right)+4\left(-8\right)+0\left(6\right)\\ u\cdot v=0+(-32)+0\\ u\cdot v=-32\end{array}$

This problem dot product is not equal to zero. Therefore, the vectors are not orthogonal.