Question

The vector in the direction of the vector $\hat{i}-2\hat{j} +2\hat{k}$ that has magnitude $9$ is

• A. $\hat{i}-2\hat{j} +2\hat{k}$
• B. $\frac{\hat{i}-2\hat{j} +2\hat{k}}{3}$
• C. $ 3\left( \hat{i}-2\hat{j} +2\hat{k}\right)$
• D. $ 9\left( \hat{i}-2\hat{j} +2\hat{k}\right)$

Answer 1

Answer: (C)

Let $\overrightarrow{a} = \hat{i}-2\hat{j} +2\hat{k}$
$\left|\vec{a}\right| = \sqrt{ 1+ 4+ 4} $
$= \sqrt{9} = 3 $
$\therefore $ Required vector $=\frac{9\left( \hat{i}-2\hat{j} +2\hat{k}\right)}{3} $
$= 3\left( \hat{i}-2\hat{j} +2\hat{k}\right)$