Question

Find a unit vector in the direction of $\overrightarrow{AB}$, where $A(1,2,3)$ and $B(4,5,6)$ are the given points.

Answer 1

We have,

$\begin{array}{c}A\left(1,2,3\right)B\left(4,5,6\right)\\ \overrightarrow{AB}=\left(3,3,3\right)\\ unitvectorindirectionof\overrightarrow{AB}=\frac{3\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{9+9+9}}\\ \overrightarrow{AB}=\frac{3\hat{i}+3\hat{j}+3\hat{k}}{\sqrt{27}}\\ =\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}+\frac{1}{\sqrt{3}}\hat{k}\end{array}$

Hence, this is the answer.