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. None of these

Answer 1

Answer: (C)

$\frac{7}{3}(\hat{i}+2\hat{j}+2\hat{k})$

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