Browse Questions

# Write the unit vector in the direction of the vector $\overrightarrow a = 2\hat i + \hat j + 2\hat k$.

Toolbox:
• Unit vector along $\overrightarrow a$ is $\large\frac{\overrightarrow a}{\mid\overrightarrow a\mid}$
Step 1:
Given :
$\overrightarrow a=2\hat i+\hat j+2\hat k$
Unit vector along $\overrightarrow a$ is $\large\frac{\overrightarrow a}{\mid\overrightarrow a\mid}$
$\mid\overrightarrow a\mid=\sqrt{2^2+1^2+2^2}$
$\qquad=\sqrt{4+1+4}$
$\qquad=\sqrt 9$
$\qquad=3$
Step 2:
$\therefore$unit vector along $\overrightarrow a=\large\frac{1}{3}$$(2\hat i+\hat j+2\hat k)$