# Write a unit vector in the direction of $$\overrightarrow a = 2\hat i - 6\hat j + 3\hat k.$$

Toolbox:
• Unit vector for a given vector $\overrightarrow a$ is $\hat n=\large\frac{\overrightarrow a}{\mid \overrightarrow a \mid}$
• $\mid \overrightarrow a\mid=\sqrt{a_1^2+a_2^2+a_3^2}$
Step 1:
Given $\overrightarrow a=2\hat i-6\hat j+3\hat k$
$\mid\overrightarrow a\mid =\sqrt{(2)^2+(-6)^2+(3)^2}$
$\quad\quad=\sqrt{4+36+9}$
$\quad\quad=7$
Step 2:
$\therefore$ unit vector along $\overrightarrow a$ is $\large\frac{1}{7}$$(2\hat i-6\hat j+3\hat k)$