Chapter 8.3, Problem 22E

To determine

To find: the ordered triple to represent $\overrightarrow{u}$ in given equation.

Answer to Problem 22E

  $\langle 18,36,2\rangle$

Explanation of Solution

Given information:

  $\begin{array}{c}\overrightarrow{w}=\langle 2,6,-1\rangle \\ \overrightarrow{z}=\langle 3,0,4\rangle \end{array}$

The given equation is shown below:

  $\overrightarrow{u}=6\overrightarrow{w}+2\overrightarrow{z}$

Calculation:

The ordered triple of $\overrightarrow{u}$ can be evaluated as follows:

  $\begin{array}{c}\overrightarrow{u}=6\overrightarrow{w}+2\overrightarrow{z}\\ =6\langle 2,6,-1\rangle +2\langle 3,0,4\rangle \left[\text{Put ordered pairs of }\overrightarrow{w}\text{ and }\overrightarrow{z}\right]\\ =\langle 12,36,-6\rangle +\langle 6,0,8\rangle \\ =\langle 12+6,36+0,-6+8\rangle \\ =\langle 18,36,2\rangle \end{array}$

Thus the ordered triple is

  $\langle 18,36,2\rangle$ .