Find a vector in the direction of vector $$\overrightarrow a = \hat i - 2\hat j$$, whose magnitude is 7.

Toolbox:
• Unit vector in the direction of $\overrightarrow a$ is $\hat a=\large\frac{\overrightarrow a}{\mid \overrightarrow a\mid}$
Given :
$\overrightarrow a=\hat i-2\hat j$
$\mid \overrightarrow a\mid=\sqrt{1^2+2^2}$
$\qquad=\sqrt 5$
The unit vector in the direction of $\overrightarrow a$ is
$\hat a=\large\frac{\overrightarrow a}{\mid \overrightarrow a\mid}$
$\quad=\large\frac{1}{\sqrt 5}$$(\hat i-2\hat j) Step 2: Therefore the vector having magnitude equal to 7,and in the direction \overrightarrow a is 7\hat a=7\big(\large\frac{\hat i-2\hat j}{\sqrt 5}\big) \quad= \large\frac{7}{\sqrt 5}$$\hat i-\large\frac{14}{\sqrt 5}$$\hat j$