The unit vector in the direction of sum of vectors $\vec{a}=2\hat{i}-\hat{j} +\hat{k}$ and $\vec{b}=2\hat{j}+\hat{k}$ is :

$\frac{2\hat{i}+\hat{j}+2\hat{k}}{3}$

The correct answer is Option (1) → $\frac{2\hat{i}+\hat{j}+2\hat{k}}{3}$

$\vec a+\vec b=2\hat i+\hat j+2\hat k=\vec v$

$|\vec v|=\sqrt{2^2+1+2^2}=3$

so $\hat v=\frac{\vec v}{|\vec v|}=\frac{2\hat{i}+\hat{j}+2\hat{k}}{3}$