Question

If $|\overrightarrow{A}|=2,|\overrightarrow{B}|=5$ and $|\overrightarrow{A}\times \overrightarrow{B}|=8$. Angle between $A$ and $B$ is acute, then $\overrightarrow{A}.\overrightarrow{B}$ is

• A. 6
• B. 3
• C. 4
• D. 7

Answer 1

The correct option is A 6

$|\overrightarrow{A}\times \overrightarrow{B}|=AB\sin \theta$
Putting the given values,
$8=\left(2\right)\left(5\right)\sin \theta$
$\therefore \sin \theta =\frac{4}{5}$ or $\cos \theta =\frac{3}{5}$
$\therefore \overrightarrow{A}.\overrightarrow{B}=AB\cos \theta =\left(2\right)\left(5\right)\left(\frac{3}{5}\right)=6$