Question

The area of the parallelogram constructed on the vectors $\overrightarrow{a}=\overrightarrow{p+}\overrightarrow{2q}$ & $\overrightarrow{b}+\overrightarrow{2p}+\overrightarrow{q}$ where $\overrightarrow{p}$ & $\overrightarrow{q}$ are unit vectors forming an acute angle of ${30}^o$ is

• A. $\frac{3}{2}$
• B. $\frac{5}{2}$
• C. $\frac{7}{2}$
• D. $None$

Answer 1

The correct option is A $\frac{3}{2}$

Area of parallologram

$=|\overrightarrow{a}\times \overrightarrow{b}|$

$=|\overrightarrow{a}|\cdot |\overrightarrow{b}|\cdot \left(\sin {30}^{\circ }\right)-(|\overrightarrow{a}|=\sqrt{1^2+2^2}=\sqrt{5})$

$=\sqrt{5}\cdot \sqrt{5}\times \frac{1}{2}$

$=\frac{5}{2}$