Question

Find $|\overrightarrow{b}|$, if $(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}-\overrightarrow{b})=8$ and $|\overrightarrow{a}|=8|\overrightarrow{b}|$.

Answer 1

$(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}-\overrightarrow{b})=8$

$|\overrightarrow{a}{|}^2-|\overrightarrow{b}{|}^2=8$

$64|\overrightarrow{b}{|}^2-|\overrightarrow{b}{|}^2=8$

$63|\overrightarrow{b}{|}^2=8$

$|\overrightarrow{b}{|}^2=\frac{8}{63}$

$|\overrightarrow{b}|=\pm \sqrt{\frac{8}{63}}$