Question

If vectors $a$ and $b$ be respectively equal to $3\hat{i}-4\hat{j}+5\hat{k}$ and $2\hat{i}+3\hat{j}-4\hat{k}$.Find the unit vector parallel to $\overrightarrow{a}+\overrightarrow{b}$.

Answer 1

Let $\overrightarrow{R}$ be resultant of $\overrightarrow{a}$ & $\overrightarrow{b}$

$\overrightarrow{a}=3\hat{i}-4\hat{j}-5\hat{k}$

$\overrightarrow{b}=2\hat{i}+3\hat{j}-4\hat{k}$

$\overrightarrow{R}=\overrightarrow{a}+\overrightarrow{b}$

$=(3+2)\hat{i}+(-4+3)\hat{j}+(5-4)\hat{k}$

$=5\hat{i}-\hat{j}+\hat{k}$

$|\overrightarrow{R}|=\sqrt{5^2+(-1{)}^2+1^2}$

$=\sqrt{25+1+1}$

$=\sqrt{27}$

$\hat{R}=\frac{\overrightarrow{R}}{|\overrightarrow{R}|}=\frac{5\hat{i}-\hat{j}+\hat{k}}{\sqrt{27}}$.