Thanks, heureka......here's another method that is vey similar to its 2D counterpart....
c (1,1,1) a (1,-4,2) b (-5,2,7)
Let vector ca = < 0, -5, 1>
Let vector cb = < -6, 1, 6 >
Find the length of ca = sqrt26]
Find the length of cb =sqrt [73]
Find the dot product of both vectors = [0*-6 + -5*1 + 1*6] = [1]
And the measure of angle acb can be found as follows :
cos[acb] = dot product of both vectors / [ product of their lengths] .......so we have
cos[acb] = 1 / sqrt[73*26]
cos-1 [ 1/sqrt[73*26] = acb ≈ 88.684736791499°
Similarly
Let vector ba = < 6,-6,-5> and its length = sqrt(97)
Let vector bc = < 6, -1, -6> and it's length = sqrt(73)
And the dot probuct of both vectors = [36 + 6 + 30] =[72]
So
cos(abc) = 72/ sqrt(97*73)
cos-1 [ 72/ sqrt(97*73)] = abc ≈ 31.17077106171°
Lastly
Let vector ab = < -6, 6, 5> and its length = sqrt(97)
Let vector ac = <0, 5, -1> and it's length = sqrt(26)
And the dot product of the two vectors = [0 + 30 - 5 ] = [25]
So
cos(bac) = 25 / sqrt(97*26)
cos-1 [ 25 / sqrt(97*26) ] = bac ≈ 60.144492146791°
Just as heureka found......
