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

1 Answer

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$
answered Sep 24, 2013 by sreemathi.v
 

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