Chapter 8.2, Problem 27E

To determine

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

Answer to Problem 27E

  $\langle -22,29\rangle$

Explanation of Solution

Given information:

  $\begin{array}{l}\overrightarrow{b}=\langle 6,3\rangle \\ \overrightarrow{c}=\langle -4,8\rangle \end{array}$

The given equation is shown below:

  $\overrightarrow{a}=-\overrightarrow{b}+4\overrightarrow{c}$

Calculation:

The ordered pair of $\overrightarrow{a}$ can be evaluated as follows:

  $\begin{array}{c}\overrightarrow{a}=-\overrightarrow{b}+4\overrightarrow{c}\\ =-\langle 6,3\rangle +4\langle -4,8\rangle \left[\text{Put ordered pairs of }\overrightarrow{b}\text{ and }\overrightarrow{c}\right]\\ =\langle -6,-3\rangle +\langle -16,32\rangle \\ =\langle -6-16,-3+32\rangle \\ =\langle -22,29\rangle \end{array}$

Thus the ordered pair is $\langle -22,29\rangle$ .