Question

Given $|\overrightarrow{a}|=10,|\overrightarrow{b}|=2$ and $\overrightarrow{a}.\overrightarrow{b}=12$, find $|\overrightarrow{a}\times \overrightarrow{b}|$.

Answer 1

$(\overrightarrow{a}.\overrightarrow{b}{)}^2+|\overrightarrow{a}\times \overrightarrow{b}{|}^2=|\overrightarrow{a}{|}^2|\overrightarrow{b}{|}^2$

Therefore,

${12}^2+|\overrightarrow{a}\times \overrightarrow{b}{|}^2=(10{)}^2\times (2{)}^2$

$|\overrightarrow{a}\times \overrightarrow{b}{|}^2=400-144=256$

$|\overrightarrow{a}\times \overrightarrow{b}|=16$