Question

Find $\overrightarrow{A}\times \overrightarrow{B}$, if $\overrightarrow{A}=3\hat{i}-\hat{j}+3\hat{k}$ and $\overrightarrow{B}=-2\hat{i}+3\hat{j}+4\hat{k}$

• A. $13\hat{i}-18\hat{j}+7\hat{k}$
• B. $-13\hat{i}-18\hat{j}-7\hat{k}$
• C. $-13\hat{i}+18\hat{j}+7\hat{k}$
• D. $-13\hat{i}-18\hat{j}+7\hat{k}$

Answer 1

The correct option is D $-13\hat{i}-18\hat{j}+7\hat{k}$

We have
$\overrightarrow{A}=3\hat{i}-\hat{j}+3\hat{k}$ and $\overrightarrow{B}=-2\hat{i}+3\hat{j}+4\hat{k}$
So, using determinant method we have
$\left[\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 3& -1& 3\\ -2& 3& 4\end{array}\right]$
$\Rightarrow (-4-9)\hat{i}-(12-(-6\left)\right)\hat{j}+(9-2)\hat{k}$
$\Rightarrow -13\hat{i}-18\hat{j}+7\hat{k}$