Question

1. Dados os vetores u = (3, −1/2, 1), v = (2, −1, 1) e w = (−2, 1, 3), calcular:
a) 2u· (v + w )
b) ( u x v ) · ( v x u )

Answer 1

Resposta:

Explicação passo a passo:

a)

2(3, -1/2, 1) . [(2, -1, 1) + (-2, 1, 3) =

(6, -1, 2) . (0, 0, 4) = 6.0 + (-1).0 + 2.4 = 8

b)

(u x v) = $\left[\begin{array}{ccc}i&j&k\\3&-1/2&1\\2&-1&1\end{array}\right] =(-1/2 +1)i+(2-3)j+(-3+1)k = -1/2i-j-2k = (1/2, -1, -2)$

(v x u) = -(u x v) = -(1/2, -1, -2) = (-1/2, 1, 2)

Logo

(u x v) . (v x u) = (1/2, -1, -2) . (-1/2, 1, 2) = [1/2 x (-1/2) + (-1) x 1 + (-2) x 2] = (-1/4 - 1 - 4) = -21/4