Question

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

• A. $15\hat{i}+6\hat{j}+12\hat{k}$
• B. $5\hat{i}+6\hat{j}-12\hat{k}$
• C. $15\hat{i}+16\hat{j}+12\hat{k}$
• D. $15\hat{i}+6\hat{j}-12\hat{k}$

Answer 1

The correct option is D $15\hat{i}+6\hat{j}-12\hat{k}$

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
$\left[\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& 4\\ 2& -3& 1\end{array}\right]$
$\Rightarrow (3-(-12\left)\right)\hat{i}-(2-8)\hat{j}+(-6-(6\left)\right)\hat{k}$
$\Rightarrow 15\hat{i}+6\hat{j}-12\hat{k}$