Chapter 8.2, Problem 14E

To determine

To find: the ordered pair and magnitude of $\overrightarrow{YZ}$ .

Answer to Problem 14E

  $\begin{array}{c}\text{Ordered pair}=\langle -2,6\rangle \\ \text{Magnitude}=2\sqrt{10}\end{array}$

Explanation of Solution

Given information:

  $Y\left(4,2\right),Z\left(2,8\right)$

Calculation:

The ordered pair of $\overrightarrow{YZ}$ is evaluated as follows:

  $\begin{array}{c}\overrightarrow{YZ}=\langle x_2-x_1,y_2-y_1\rangle \\ =\langle 2-4,8-2\rangle \left[\text{Put ordered pairs of }Z\text{ and }Y\right]\\ =\langle -2,6\rangle \end{array}$

Thus the ordered pair is $\langle -2,6\rangle$ .

The magnitude of $\overrightarrow{YZ}$ is evaluated as follows:

  $\begin{array}{c}\left|\overrightarrow{YZ}\right|=\sqrt{{\left({\overrightarrow{YZ}}_x\right)}^2+{\left({\overrightarrow{YZ}}_y\right)}^2}\\ =\sqrt{{\left(-2\right)}^2+{\left(6\right)}^2}\left[\text{Put the ordered pairs of }\overrightarrow{YZ}\right]\\ =\sqrt{40}\\ =2\sqrt{10}\end{array}$

Thus the magnitude is $2\sqrt{10}$ .