Question

Find the unit vector in the direction of the vector $\vec{a}=\hat{i}+\hat{j}+2\hat{k}.$

Answer 1

The correct answer is:$\frac{1}{\sqrt{6}\hat{i}}+\frac{1}{\sqrt{6}\hat{j}}+\frac{2}{\sqrt{6}\hat{k}}.$
The unit vector $\hat{a}$ in the direction of vector $\vec{a}=\hat{i}+\hat{j}+2\hat{k}$ is given by $\hat{a}=\frac{\vec{a}}{|a|}.$
$|\vec{a}|=\sqrt{1^2+1^2+2^2}=\sqrt{1+1+4}=\sqrt6$
$∴\hat{a}=\frac{\vec{a}}{|\vec{a}|}=\frac{\hat{i}+\hat{j}+2\hat{k}}{\sqrt6}=\frac{1}{\sqrt{6}\hat{i}}+\frac{1}{\sqrt{6}\hat{j}}+\frac{2}{\sqrt{6}\hat{k}}.$