Question

If $\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{b}=3\hat{i}+6\hat{j}+2\hat{k}$, then the vector in the direction of $\overrightarrow{a}$ and having magnitude as $|\overrightarrow{b}|$, is

• A. $7(\hat{i}+2\hat{j}+2\hat{k})$
• B. $\frac{7}{9}(\hat{i}+2\hat{j}+2\hat{k})$
• C. $\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$
• D. $Noneofthese$

Answer 1

The correct option is C $\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$

The required vectors
$=|\overrightarrow{b}|\hat{a}=\frac{|\overrightarrow{b}|}{|\overrightarrow{a}|}\overrightarrow{a}=\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$