+128475 This doesn't work much differently than in 2 space.....we can still use the Law of Cosines
BC = sqrt [ (2 - 4)^2 + (-2 -4)^2 + (2 - 4)^2 ] = sqrt [ 4 + 36 + 4] = sqrt (44)
AC = sqrt [ (1 - 4)^2 + (0 - 4)^2 + (2 - 2)^2] = sqrt ( 9 + 16) = sqrt (25) =5
AB = sqrt [ (1 - 2)^2 + (-2 - 0)^2 + ( 4 - 2)^2 ] = sqrt [ 1 + 4 + 4 ] = sqrt (9) = 3
So....we have that
BC^2 = AC^2 + AB^2 - 2 ( AC)(AB) cos (BAC)
44 = 25 + 9 - 2 (5)(3) cos (BAC)
[44 - 25 - 9] / [ -2 * 5 * 3 ] = cos (BAC)
cos (BAC) = 10 / [ - 30 ] = -1/3
