Question

Let a and 2b denote the diagonals of a parallelogram. Then area of the parallelogram is given by

• A. $|a\times b|$
• B. $\frac{1}{2}|a\times b|$
• C. $2|a\times b|$
• D. None of these

Answer 1

The correct option is A $|a\times b|$

Area of parallelogram with diagonals $\overrightarrow{d_1},\overrightarrow{d_2}$ is given by, $\frac{1}{2}|\overrightarrow{d_1}\times \overrightarrow{d_2}|$
Hence area of parallelogram with diagonal $a$ and $2b$ is given by, $\frac{1}{2}|a\times 2b|=|a\times b|$