Question

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

Answer 1

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

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

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

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

$\overrightarrow{|b|}=\frac{2\sqrt{2}}{3\sqrt{7}}$