Question

Write a unit vector in the direction of \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\].

Answer 1

Given: \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\]
\[\left| \overrightarrow{b} \right| = \sqrt{2^2 + 1^2 + 2^2} = \sqrt{4 + 1 + 4} = \sqrt{9} = 3\]
∴ Unit vector = \[\frac{\overrightarrow{b}}{\left| \overrightarrow{b} \right|} = \frac{1}{3}\left( 2 \hat{i} + \hat{j} + 2 \hat{k} \right) = \frac{2}{3} \hat{i} + \frac{1}{3} \stackrel\frown{j} + \frac{2}{3} \hat{k}\]