Question

Calculate the area of the parallelogram when adjacent sides are given by the vectors $\overrightarrow{A}=\hat{i}-\hat{j}+2\hat{k}$ and $\overrightarrow{B}=2\hat{i}-3\hat{j}+4\hat{k}$

• A. $2\hat{i}-\hat{k}$
• B. $-2\hat{i}-\hat{k}$
• C. $2\hat{i}+\hat{k}$
• D. $2\hat{i}-2\hat{k}$

Answer 1

The correct option is A $2\hat{i}-\hat{k}$

We know that the area of parallelogram is given by $\overrightarrow{A}\times \overrightarrow{B}$, where vectors are the adjacent sides.
Thus, area of parallelogram is given by
$\left[\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 1& -1& 2\\ 2& -3& 4\end{array}\right]$
$\Rightarrow (-4-(-6\left)\right)\hat{i}-(4-4)\hat{j}+(-3-(-2\left)\right)\hat{k}$
$\Rightarrow 2\hat{i}-\hat{k}$