Q. If the area of the parallelogram with $\overrightarrow{\mathbf{a}}\ and\ \overrightarrow{\mathbf{b}}$ as two adjacent side is 15 sq units, then the area of the parallelogram having $3\overrightarrow{\mathbf{a}} + 2\overrightarrow{\mathbf{b}}$ and$\overrightarrow{\mathbf{a}} + 3\overrightarrow{\mathbf{b}}$ as two adjacent sides in sq units is
A) 120
B) 105
C) 75
D) 45
Explanation
(b)
Given , area $= |\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}| = 15$
If the sides are $\left( 3\overrightarrow{\mathbf{a}} + 2\overrightarrow{\mathbf{b}} \right)and\ \left( \overrightarrow{\mathbf{a}} + 3\overrightarrow{\mathbf{b}} \right),$ then
Area of parallelogram
$= \left| \left( 3\overrightarrow{\mathbf{a}} + 2\overrightarrow{\mathbf{b}} \right) \times \left( \overrightarrow{\mathbf{a}} + 3\overrightarrow{\mathbf{b}} \right) \right| = 7\left| \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right|$
$= 7 \times 15 = 105$ sq units
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.