Question

Dado os vetores u=(1, a, -2a-1), v=(a, a-1, 1) e w=(a,-1,1)

Determinar "a" de modo que u.v=(u+v).w

Answer 1

$u*v\\ (1, a, -2a - 1) * (a, a-1, 1) = a^2 -2a - 1 \\ \\ \\ u+v \\ (1, a, -2a - 1)+(a, a-1, 1) = (a, 2a -1, -2a)$

$(u+v)*w \\ (a, 2a -1, -2a)*(a, -1, 1) = a^2 - 4a + 1$

$u*v=(u+v)*w \\ a^2 -2a - 1 = a^2 - 4a + 1 => 2a = 2 => a = 2/2 => a = 1$

Resposta = a = 1