Browse Questions

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

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