Chapter 8.3, Problem 29E

To determine

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

Answer to Problem 29E

  $3\overrightarrow{i}-8\overrightarrow{j}-5\overrightarrow{k}$

Explanation of Solution

Given information:

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

Calculation:

The sum of unit vector can be evaluated as follows:

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

Thus the sum unit of vector is $3\overrightarrow{i}-8\overrightarrow{j}-5\overrightarrow{k}$ .