Question

Let $\overrightarrow{a}=4\hat{i}+3\hat{j}+\hat{k},\overrightarrow{b}=2\hat{i}+\hat{j}+2\hat{k}$ and $\overrightarrow{c}=6\hat{i}-2\hat{j}-3\hat{k}$ be three vectors. Then the magnitude of projection of $\overrightarrow{a}\times \overrightarrow{b}$ on $\overrightarrow{c}$ is

• A. 7
• B. $\frac{48}{7}$
• C. $\frac{45}{7}$
• D. $\frac{43}{7}$

Answer 1

The correct option is B $\frac{48}{7}$

$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{i}\\ 4& 3& 1\\ 2& 1& 2\end{array}\right|$
$=\hat{i}\left(5\right)-\hat{j}\left(6\right)+\hat{k}(-2)=5\hat{i}-6\hat{j}-2\hat{k}$
Projection of $\overrightarrow{a}\times \overrightarrow{b}on\overrightarrow{c}=\frac{|\overrightarrow{a}\times \overrightarrow{b}.\overrightarrow{c}|}{|\overrightarrow{c}|}=\frac{30+12+6}{7}=\frac{48}{7}$