Question

The adjacent sides of a parallelogram are represented by co-initial vectors $2\widehat{i} + 3\widehat{j}$ and $\widehat{i} + 4\widehat{j}$. The area of the parallelogram is–

• A. (a) 5 units along z-axis
• A. (b) 5 units in x-y plane
• A. (c) 3 units in x-z plane
• A. (d) 3 units in y-z plane

Answer 1

(a)

$\overrightarrow{A}$×$\overrightarrow{B}$ = $\left| \begin{matrix} \widehat{i} & \widehat{j} & \widehat{k} \\ 2 & 3 & 0 \\ 1 & 4 & 0 \end{matrix} \right|$ = $\widehat{k}$ (8 – 3) = 5$\widehat{k}$