Chapter 8.3, Problem 32E

To determine

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

Answer to Problem 32E

  $-20\overrightarrow{i}+5\overrightarrow{j}-11\overrightarrow{k}$

Explanation of Solution

Given information:

  $L\left(12,2,6\right)\text{ and }B\left(-8,7,-5\right)$ .

Calculation:

The sum of unit vector can be evaluated as follows:

  $\begin{array}{c}\overrightarrow{LB}=\left(x_2-x_1\right)\overrightarrow{i}+\left(y_2-y_1\right)\overrightarrow{j}+\left(z_2-z_1\right)\overrightarrow{k}\\ =\left(-8-12\right)\overrightarrow{i}+\left(7-2\right)\overrightarrow{j}+\left(-5-6\right)\overrightarrow{k}\left[\begin{array}{l}\text{Put }{x}_1=12,y_1=2,z_1=6,\\ x_2=-8,y_2=7\text{ and }{z}_2=-5\end{array}\right]\\ =-20\overrightarrow{i}+5\overrightarrow{j}-11\overrightarrow{k}\end{array}$

Thus the sum of unit vectors is $-20\overrightarrow{i}+5\overrightarrow{j}-11\overrightarrow{k}$ .