Question

Calcule a projeção dos vetores AB (1,0,1) sobre BC (0,-1,-2) OBS álgebra vetorial.

Answer 1

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$\Large\boxed{\sf{\underline{Projec_{\!\!,}\tilde{a}o~de~um~vetor}}}$

$\boxed{\sf{proj_{\overrightarrow{v}}\overrightarrow{u}=\left(\dfrac{\overrightarrow{u}\cdot\overrightarrow{v}}{\overrightarrow{v}\cdot\overrightarrow{v}}\right)\cdot\overrightarrow{v}}}$

$\sf{\overrightarrow{u}=(1,0,1)~~\overrightarrow{v}=(0,-1,-2)}\\\sf{\overrightarrow{u}\cdot\overrightarrow{v}=1\cdot0+0\cdot(-1)+1\cdot(-2)=-2}\\\sf{\overrightarrow{v}\cdot\overrightarrow{v}=0\cdot0-1\cdot(-1)-2\cdot(-2)=1+4=5}$

$\sf{proj_{\overrightarrow{v}}\overrightarrow{u}=-\dfrac{2}{5}\cdot(0,-1,-2)=(0,\dfrac{2}{5},\dfrac{4}{5})}$