Chapter 8.2, Problem 35E

To determine

To find: the sum of the vector by using the given information.

Answer to Problem 35E

  $\langle -30,4.5\rangle$

Explanation of Solution

Given information:

  $\begin{array}{l}\overrightarrow{m}=\langle -5,-6\rangle \\ \overrightarrow{n}=\langle 6,-9\rangle \end{array}$

Let the sum of the vector be $\overrightarrow{a}$ .

The given condition is shown below:

  $\overrightarrow{a}=3\overrightarrow{m}+2\frac{1}{2}\left(-\overrightarrow{n}\right)$

Calculation:

The vector $\overrightarrow{a}$ can be evaluated as follows:

  $\begin{array}{c}\overrightarrow{a}=3\overrightarrow{m}+2\frac{1}{2}\left(-\overrightarrow{n}\right)\\ =3\overrightarrow{m}-\frac{5}{2}\overrightarrow{n}\\ =3\overrightarrow{m}-2.5\overrightarrow{n}\\ =3\langle -5,-6\rangle -2.5\langle 6,-9\rangle \left[\text{Put ordered pairs of }\overrightarrow{m}\text{ and }\overrightarrow{n}\right]\\ =\langle -15,-18\rangle -\langle 15,-22.5\rangle \\ =\langle -15-\left(-15\right),-18-\left(-22.5\right)\rangle \\ =\langle -30,4.5\rangle \end{array}$

Thus the ordered pair is $\langle -30,4.5\rangle$ .