Question

calcule a projeção do vetor AC (1,4,-1) sobre o vetor BD(0,-2,-1)

Answer 1

$\displaystyle \mbox{Proy}_{(0,-2,-1)}(1,4,-1)=\frac{(1,4,-1)\cdot (0,-2,-1)}{\|(0,-2,-1)\|^2}\cdot (0,-2,-1)\\ \\ \\ \mbox{Proy}_{(0,-2,-1)}(1,4,-1)=-\frac{7}{5}\cdot (0,-2,-1)\\ \\ \\ \boxed{\mbox{Proy}_{(0,-2,-1)}(1,4,-1)= \left(0,\frac{14}{5},\frac{7}{5}\right)}$