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.