v = 2 n_x + 3 n_y + 4 n_z w = 5 n_x + -6 n_y + 7 n_z 10v = 20 n_x + 30 n_y + 40 n_z v/10 = 0.2 n_x + 0.3 n_y + 0.4 n_z v + w = 7 n_x + -3 n_y + 11 n_z v - w = -3 n_x + 9 n_y + -3 n_z dot(v,w) = 20 cross(v,w) = 45 n_x + 6 n_y + -27 n_z cross(w,v) = -45 n_x + -6 n_y + 27 n_z v^2 = 29 v^3 = 58 n_x + 87 n_y + 116 n_z magnitude(v) = 5.3852 magnitude(w) = 10.488 unit(v) = 0.371391 n_x + 0.557086 n_y + 0.742781 n_z angle between v and w (rad) = 1.2088 angle between v and w (deg) = 69.261 v * w = [ 10 -12 14 ] [ 15 -18 21 ] [ 20 -24 28 ] w * v = [ 10 15 20 ] [ -12 -18 -24 ] [ 14 21 28 ]