Question

A parallelogram has diagonals expressed as $\overrightarrow{A} = 5\widehat{i} - 4\widehat{j} + 3\widehat{k}$ and $\overrightarrow{B} = 3\widehat{i} + 2\widehat{j} - \widehat{k}$. Area of parallelogram is

• A. (a)$\sqrt{117}$ units
• A. (b)$\sqrt{171}$ units
• A. (c)$\sqrt{711}$ units
• A. (d)$\sqrt{107}$ units

Answer 1

(b)

$\left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 5 & - 4 & 3 \\ 3 & 2 & - 1 \end{matrix} \right|$

$\overrightarrow{A} \times \overrightarrow{B}$ = -2$\widehat{i}$ + 14$\widehat{j}$ + 22$\widehat{k}$

Area = 1/2 |$\overrightarrow{A} \times \overrightarrow{B}$| = $\sqrt{1^{2} + 7^{2} + 11^{2}}$ = $\sqrt{171}$ unit