Question

Encontre a projeção do vetor a sobre b, sendo a = (0, 2, −1) e b = (1, 1, 3):

Answer 1

$\text{proj}^a_b=\frac{a\cdot b}{b\cdot b}\;b$

$\text{proj}^a_b=\frac{(0,2,-1)\cdot (1,1,3)}{(1,1,3)\cdot (1,1,3)}\;(1,1,3)$

$\text{proj}^a_b=\frac{0\cdot1+2\cdot1+(-1)\cdot3}{1\cdot1+1\cdot1+3\cdot3}\;(1,1,3)$

$\text{proj}^a_b=\frac{-1}{11}\;(1,1,3)$

$\text{proj}^a_b=\left(-\frac{1}{11},-\frac{1}{11},-\frac{3}{11}\right)$