Question

Sendo |u+v|=7 e |u-v|=5 calcule u.v

Answer 1

$|\overrightarrow{u}+\overrightarrow{v}|=7$

$|\overrightarrow{u}-\overrightarrow{v}|=5$

Elevando tudo ao quadrado

$|\overrightarrow{u}+\overrightarrow{v}|^2=7^2$

$|\overrightarrow{u}-\overrightarrow{v}|^2=5^2$

$|\overrightarrow{u}|^2+2*\overrightarrow{u}\cdot\overrightarrow{v}+|\overrightarrow{v}|^2=49$

$|\overrightarrow{u}|^2-2*\overrightarrow{u}\cdot\overrightarrow{v}+|\overrightarrow{v}|^2=25$

Subtraindo o de baixo pelo de cima

$4*\overrightarrow{u}\cdot\overrightarrow{v}=24$

$\maltese~\overrightarrow{u}\cdot\overrightarrow{v}=6~\maltese$