Question

If $|\overrightarrow{a}\times \overrightarrow{b}|$ =16, $|\overrightarrow{a}|$ = 10 and $\overrightarrow{a}.\overrightarrow{b}$=12 find $|\overrightarrow{b}|$.

Answer 1

$|\overline{a}\times \overline{b}|=16;\left|\overline{a}\right|=10;|\overline{a}\cdot \overline{b}|=12$

$ab\sin \theta =16\to 1ab\cos \theta =12\to 2$

Dividing equations $1/2$

$\frac{\sin \theta }{\cos \theta }=\frac{16}{12}=\frac{4}{3}$

$\tan \theta =\frac{4}{3}$

$\sin \theta =4/5$

$ab\sin \theta =16$

$10\times b\times \frac{4}{5}=16$

$b=\frac{16\times 5}{10\times 4}=2$

$\therefore \left|\overline{b}\right|=2$