Question

Find $\overrightarrow{A}.\overrightarrow{B}$ if $\left|\overrightarrow{A}\right|=2,\left|\overrightarrow{B}\right|=5$ and $|\overrightarrow{A}\times \overrightarrow{B}|=8$

Answer 1

Given $|A|=2$

$|B|=5$

$|A\times B|=8$

we know that

$|A\times B|=|A||B|\sin \theta$

So, $2\times 5\times \sin \theta =8$

$\Rightarrow \sin \theta =\frac{4}{5}$

$\Rightarrow \cos \theta =\dfrac{3}{5}$

So,

$|A||B|\cos \theta$

$\Rightarrow A.B=2\times 5\times \frac{3}{5}$

$\Rightarrow A.B=6$