Question

The diagonals of parallelogram are given by the vectors $2\hat{i}+3\hat{j}-6\hat{k}$ and $3\hat{i}-4\hat{j}-\hat{k}$, then the area of the parallelogram is

• A. $\frac{1}{2}\sqrt{1274}$
• B. $\sqrt{1274}$
• C. $\frac{1}{4}\sqrt{1274}$
• D. $1274$

Answer 1

Answer: (A)

$\frac{1}{2}\sqrt{1274}$

Area of parallelogram $=\frac{1}{2}|d_1\times d_2|$

$=\frac{1}{2}\left|\left[\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& -6\\ 3& -4& -1\end{array}\right]\right|$

$=\frac{1}{2}\sqrt{1274}$ sq units