Question

Dados os vetores u=(2,3,4) e v=(a,2,3), determinar a norma da projeção de u sobre v.

Answer 1

$proj_vu=\dfrac{u\cdot v}{v\cdot v}v\\\\\\proj_vu=\dfrac{(2 ,3 ,4)\cdot (a,2,3)}{(a,2,3)\cdot (a,2,3)}(a,2,3)=\dfrac{2a+6+12}{a^2+4+9}(a,2,3)=\\\\\dfrac{2a+18}{a^2+13}(a,2,3)=(\dfrac{2a^2+18a}{a^2+13},\dfrac{4a+36}{a^2+13},\dfrac{6a+54}{a^2+13})$