Question

The area of parallegram represented by the vectors. $\overrightarrow{A}=2\stackrel{\wedge }{i}+3\stackrel{\wedge }{j}$ and $\overrightarrow{B}=\stackrel{\wedge }{i}+4\stackrel{\wedge }{j}$ is :-

• A. 14 units
• B. 7.5 units
• C. 10 units
• D. 5 units

Answer 1

The correct option is D 5 units

The area of the parallelogram is given by, $a=|\overrightarrow{A}\times \overrightarrow{B}|$

So, $\overrightarrow{A}\times \overrightarrow{B}=(2\hat{i}+3\hat{j})\times (\hat{i}+4\hat{j})=0-3\hat{k}+8\hat{k}+0=5\hat{k}$

Thus, $a=|\overrightarrow{A}\times \overrightarrow{B}|=\sqrt{5^2}=5$ units