Question

If $\left|\overrightarrow{a}\right|=5,|\overrightarrow{a}-\overrightarrow{b}|=8$ and $|\overrightarrow{a}+\overrightarrow{b}|=10$, then $\left|\overrightarrow{b}\right|$ is equal to

Answer 1

$\left|a\right|=5;|\overline{a}-\overline{b}|=8$

[$|a+b|=10$)

${\left|a\right|}^2+{\left|b\right|}^2-2\overline{a}\overline{b}=64$

${\left|a\right|}^2+{\left|b\right|}^2-2\overline{a}\overline{b}=100$

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$2({\left|a\right|}^2+{\left|b\right|}^2)=164\Rightarrow ({\left|a\right|}^2+{\left|b\right|}^2)=82$

$25+{\left|b\right|}^2=82\Rightarrow {\left|b\right|}^2=57\Rightarrow \left|b\right|=\sqrt{57}$