Baaasic Vectors. Determine the angles within a triangle

[kjf]

Hey guys, I'm not posting this up so I don't have to do it, I've done all of the calculations and everything and have a pretty reasonable idea on what I'm doing, but I'm just getting wrong answers.

 

Triangle has 3 points (1, 0, 1), (6, 2, -7), (3, -2, 2).

I named my points A, B and C respectively.

 

I calculated AB, AC, BC and got

 

AB = (-5, -2, 7)

AC = (-2, 2, -1)

CB = (-3, -4, 9)

 

 

I then calculated magnitudes of each

 

||AB|| = sqrt 78

||AC|| = 3

||CB|| = sqrt 106

 

Dot Products were calculated aswell

 

AB.AC = 15

AC.CB = -7

AB.CB = 86

 

Cos(theta) = AB.AC / ||AB||.||AC||

Solved for theta and got 55.51

 

For AC and CB theta was 103.09

 

And finally AB and CB was 18.95

 

Which added up to approx 177 =/= 180.

 

So I don't know what I'm doing wrong? I thought I had all of my working correct?

 

If you guys could shed some light I'd greatly appreciate it, I dunno where I'm going wrong!?

 

 

Cheers,

 

Karl

[sanctus]

Just looking at it quickly AB should be (-5,-2,8) and not 7 in z-entry. Tell me, if that makes you get [math]180^\circ[/math]...