Compute wu times v where u i j k v 2i 5j 2k and w 4i

Compute w*(u times v) where u = i + j - k, v = 2i + 5j -2k and w = 4i + 7j - 4k.

Solution

U × V = ijka_xa_ya_zb_xb_yb_z = ijk11-125-2 = i (1·(-2) - (-1)·5) - j (1·(-2) - (-1)·2) + k (1·5 - 1·2) =

= i (-2 + 5) - j (-2 + 2) + k (5 - 2) = {3; 0; 3}

W · (U×V) = a_x · b_x + a_y · b_y + a_z · b_z = 4 · 3 + 7 · 0 + (-4) · 3 = 12 + 0 - 12 = 0