Question

determine a soma das coordenadas do vetor projecao de u=(7,0,3) na direçaão de v=(-1,6,-5)

Answer 1

Olá!
 
    
     Lembrando que  

$\text{Proj}_vu=\dfrac{<u,v>}{||v||^2}v,$
temos



$\text{Proj}_vu=\dfrac{\ \textless \ u,v\ \textgreater \ }{||v||^2}v =\dfrac{\ \textless \ (7,0,3),(-1,6,-5)\ \textgreater \ }{||(-1,6,-5)||^2}(-1,6,-5)=\\ \\ \\ = \dfrac{-7+0-15}{1+36+25}(-1,6,-5)=-\dfrac{22}{62}(-1,6,-5)= -\dfrac{11}{31}(-1,6,-5) = \\ \\ \\ = \left(\dfrac{11}{31},-\dfrac{66}{31},\dfrac{55}{31}\right).\\ \\ \\ \text{Portanto, tal soma vale }\\ \\ \dfrac{11-66+55}{31}=\dfrac{0}{31}=0.$



Bons estudos!