Q. 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) 5 units along $z$-axis
B) 5 units in $x - y$ plane
C) 3 units in $x - z$ plane
D) 3 units in $y - z$ plane
Explanation
(a) $\overrightarrow{A} \times \overrightarrow{B} = \left( 2\widehat{i} + 3\widehat{j} \right) \times (\widehat{i} + 4\widehat{j})$
$= 8\left( \widehat{i} \times \widehat{j} \right) + 3\left( \widehat{j} \times \widehat{i} \right) = 8\widehat{k} - 3\widehat{k} = 5\widehat{k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.