Chapter 8.3, Problem 33E

To determine

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

Answer to Problem 33E

  $-7\overrightarrow{i}+3\overrightarrow{j}-6\overrightarrow{k}$

Explanation of Solution

Given information:

  $L\left(-1,2,-4\right)\text{ and }B\left(-8,5,-10\right)$ .

Calculation:

The sum of unit vector can be evaluated as follows:

  $\begin{array}{c}\overrightarrow{LB}=\left(x_2-x_1\right)\overrightarrow{i}+\left(y_2-y_1\right)\overrightarrow{j}+\left(z_2-z_1\right)\overrightarrow{k}\\ =\left(-8-\left(-1\right)\right)\overrightarrow{i}+\left(5-2\right)\overrightarrow{j}+\left(-10-\left(-4\right)\right)\overrightarrow{k}\left[\begin{array}{l}\text{Put }{x}_1=-1,y_1=2,z_1=-4,\\ x_2=-8y_2=5\text{ and }{z}_2=-10\end{array}\right]\\ =-7\overrightarrow{i}+3\overrightarrow{j}-6\overrightarrow{k}\end{array}$

Thus the sum of unit vector is $-7\overrightarrow{i}+3\overrightarrow{j}-6\overrightarrow{k}$ .