Question

A projeção ortogonal de u ⃗ =(-2,2,1) na direção de V ⃗=(1,-2,2) é:

A) proj(_ v ⃗^( u ⃗))= 4/9 (1,-2,2)
B) proj(_ v ⃗^( u ⃗))= 4/3 (1,2,2)
C) proj(_ v ⃗^( u ⃗))= (-4)/9 (1,-2,2)
D) proj(_ v ⃗^( u ⃗))= (-4)/3 (1,2,-2)
E) proj(_ v ⃗^( u ⃗))= 4/3 (1,2,-2)

Answer 1

$\\ Proj_{ u} v = \frac{u*v}{|v|^2} *v \\ \\ Proj_{ u} v = \frac{(-2, 2, 1)(1, -2, 2)}{ (\sqrt{1^2+(-2)^2+2^2})^2 } *(1,-2, 2) \\ \\ Proj_{ u} v = \frac{-2*1+2*-2+1*2}{1+4+4} *(1,-2,2) \\ \\ Proj_{ u} v = \frac{-2-4+2}{9} *(1,-2,2) \\ \\ Proj_{ u} v = = \frac{-4}{9} *(1,-2,2)$

$LETRA = C$