Question

2) Dados os vetores u = (2, -1, 1) v = (1, -1, 0) e w = (-1, 2, 2), calcular:a) w x vb) v x (w – u)c) (u + v) x (u – v)d) (2u) x (3v)

Answer 1

a)
$wxv= \left[\begin{array}{ccc}i&j&k\\-1&2&2\\1&-1&0\end{array}\right] =i*(0+2)+j(2-0)+k(1-2)=(2,2,-1)$

b)
w - u = (-1, 2, 2) - (2, -1, 1) = (-3, 3, 1)
$(v)x(w-u)= \left[\begin{array}{ccc}i&j&k\\1&-1&0\\-3&3&1\end{array}\right] =\\\\i*(-1-0)+j*(0-1)+k*(3 - 3) = (-1, -1, 0)$

c)
u + v = (2, -1, 1) + (1, -1, 0) = (3, -2, 1)
u - v = (2, -1, 1) - (1, -1, 0) = (1, 0, 1)
$(u+v)x(u-v)= \left[\begin{array}{ccc}i&j&k\\3&-2&1\\1&0&1\end{array}\right] =\\\\i*(-2-0)+j*(1-3)+k*(0 + 2) = (-2, -2, 2)$

d)
2u = 2*(2, -1, 1) = (4, -2, 2)
3v = 3*(1, -1, 0) = (3, -3, 0)
$(2u)x(3v)= \left[\begin{array}{ccc}i&j&k\\4&-2&2\\3&-3&0\end{array}\right] =\\\\i*(0+6)+j*(6-0)+k*(-12 + 6) = (6, 6, -6)$