Question

ABCD is a quadrilateral with $\overline{AB} = \overline{a}, \overline{AD} = \overline{b}$ and $\overline{AC} = 2\overline{a} + 3\overline{b}$. If its area is $\alpha$ times the area of the parallelogram with AB, AD as adjacent sides, then the value of $\alpha$ is

• A. $\frac{1}{2}$
• B. $\frac{5}{2}$
• C. $\frac{3}{2}$
• D. 2

Hint:

Area of $\triangle$ with vectors $\vec{u}, \vec{v}$ is $\frac{1}{2}|\vec{u} \times \vec{v}|$.

Answer 1

The Correct Option is B