The unit vector in the direction of $\vec{a}+\vec{b}$ if $\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}$ & $\vec{b}=-\hat{i}+\hat{j}+-\hat{k}$ is :
Answer & explanation
Correct answer: option 4
$\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}$
$\vec{b}=-\hat{i}+\hat{j}-\bar{k}$
$\vec{a}+\vec{b}=\hat{i}+\hat{k}$
So unit vector in direction of $(\vec{a}+\vec{b})$
$=\frac{\vec{a}+\vec{b}}{|\vec{a}+\vec{b}|}=\frac{\hat{i}+\hat{k}}{\sqrt{1+1}}$
$=\frac{\hat{i}}{\sqrt{2}}+\frac{\hat{k}}{\sqrt{2}}$