Chapter 8.3, Problem 9CFU

To determine

To find: $\overrightarrow{EF}$ as the sum of unit vectors.

Answer to Problem 9CFU

  $11\overrightarrow{i}-4\overrightarrow{j}+2\overrightarrow{k}$

Explanation of Solution

Given information:

  $E\left(-5,-2,4\right)\text{ and }F\left(6,-6,6\right)$ .

Calculation:

The sum of unit vector can be evaluated as follows:

  $\begin{array}{c}\overrightarrow{EF}=\left(x_2-x_1\right)\overrightarrow{i}+\left(y_2-y_1\right)\overrightarrow{j}+\left(z_2-z_1\right)\overrightarrow{k}\\ =\left(6-\left(-5\right)\right)\overrightarrow{i}+\left(-6-\left(-2\right)\right)\overrightarrow{j}+\left(6-4\right)\overrightarrow{k}\left[\begin{array}{l}\text{Put }{x}_1=-5,y_1=-2,z_1=4,\\ x_2=6,y_2=-6\text{ and }{z}_2=6\end{array}\right]\\ =11\overrightarrow{i}-4\overrightarrow{j}+2\overrightarrow{k}\end{array}$

Thus the sum of unit vectors is $11\overrightarrow{i}-4\overrightarrow{j}+2\overrightarrow{k}$ .