The Answer Worked Out

In tedious detail:

1. The two vectors are:

   p  =  ( -2, 4, 3)^T

   q  =  ( 3, 1, -4)^T

2. The lengths are:

   |p|²  =  ( -2, 4, 3)^T · ( -2, 4, 3)^T  =  4 + 16 + 9  =  29

   |q|²  =  ( 3, 1, -4)^T · ( 3, 1, -4)^T  =  9 + 1 + 16  =  26

3. The normalized vectors are:

   p_u  =  (-2, 4, 3)^T/ 29

   q_u  =  (3, 1, -4)^T/ 26

4. The dot product is:

   p_u · q_u  =  (-2, 4, 3)·(3, 1, -4)^T/ (29 26)

     =   (-6 + 4 - 12)/(29 26)   =  -14/(29 26)  =  -0.50985

5. The angle is:

   cos θ   =  -0.50985

   θ  =  arc cos( -0.50985)  =  120.654°

Looks about correct.