Question

If $|\overline{a}|=2,|\overline{b}|=5$ and $|\overline{a}\times \overline{b}|=8$, then $|\overline{a}\cdot \overline{b}|$ is equal to.

Answer 1

$|a\cdot b{|}^2=(|a||b|{)}^2-|a\times b{|}^2$

$|a\cdot b{|}^2=(2\times 5{)}^2-(8{)}^2$

$|a\cdot b{|}^2=(10{)}^2-(8{)}^2$

$|a\cdot b{|}^2=(6{)}^2$

$|a\cdot b|=6$.