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 \(\hat{a}=\frac{\vec{a}}{|a|}.\)
\(|\vec{a}|=\sqrt{1^2+1^2+2^2}=\sqrt{1+1+4}=\sqrt6\)
\(∴\hat{a}=\frac{\vec{a}}{|\vec{a}|}=\frac{\hat{i}+\hat{j}+2\hat{k}}{\sqrt6}=\frac{1}{\sqrt{6}\hat{i}}+\frac{1}{\sqrt{6}\hat{j}}+\frac{2}{\sqrt{6}\hat{k}}.\)