Question

If $\overrightarrow{a}$ is a collinear vector with $\overrightarrow{b}=3\hat{i}+6\hat{j}+6\hat{k}$
and $\overrightarrow{a}.\overrightarrow{b}=27$. Then, $\overrightarrow{a}$ is

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

Answer 1

The correct option is C $\hat{i}+2\hat{j}+2\hat{k}$

As $\overrightarrow{a}$ is collinear to $\overrightarrow{b}$
So,
$\overrightarrow{a}=\lambda \overrightarrow{b}\Rightarrow \overrightarrow{a}.\overrightarrow{b}=\lambda \overrightarrow{b}.\overrightarrow{b}=279\lambda +36\lambda +36\lambda =27\lambda =\frac{1}{3}\Rightarrow \overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k}$