Chapter 8.3, Problem 21E

To determine

To find: the ordered pair and magnitude of $\overrightarrow{CJ}$ with the help of given graph.

Answer to Problem 21E

  $\begin{array}{c}\text{Ordered pair}=\langle 4,-8,-14\rangle \\ \text{Magnitude}=2\sqrt{69}\end{array}$

Explanation of Solution

Given information:

  $C\left(-1,3,10\right),J\left(3,-5,-4\right)$

Calculation:

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

  $\begin{array}{c}\overrightarrow{CJ}=\langle x_2-x_1,y_2-y_1,z_2-z_1\rangle \\ =\langle 3-\left(-1\right),-5-3,-4-10\rangle \left[\text{Put ordered pairs of }J\text{ and }C\right]\\ =\langle 4,-8,-14\rangle \end{array}$

Thus the ordered pair is $\langle 4,-8,-14\rangle$ .

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

  $\begin{array}{c}\left|\overrightarrow{CJ}\right|=\sqrt{{\left({\overrightarrow{CJ}}_x\right)}^2+{\left({\overrightarrow{CJ}}_y\right)}^2+{\left({\overrightarrow{CJ}}_z\right)}^2}\\ =\sqrt{{\left(4\right)}^2+{\left(-8\right)}^2+{\left(-14\right)}^2}\left[\text{Put the ordered pairs of }\overrightarrow{CJ}\right]\\ =\sqrt{16+64+196}\\ =\sqrt{276}\\ =2\sqrt{69}\end{array}$

Thus the magnitude is $2\sqrt{69}$ .