Applying the Formula

Lets see how close my guess is:

1. The two vectors are represented by:
   • f  =  (2, 4, 6)^T
   • g  =  (6, 4, 3)^T
2. The lengths are:
   • | f |²  =  (2, 4, 6)^T · (2, 4, 6)^T  =  4 + 16 + 36  =  56
   • | g |²  =  (6, 4, 3)^T · (6, 4, 3)^T  =  36 + 16 + 9  =  61
3. The normalized vectors are:
   • f_u  =   (2, 4, 6)^T / √56
   • g_u  =   (6, 4, 3)^T / √61
4. The dot product is:
   • f_u · g_u  =   (2, 4, 6)^T · (6, 4, 3)^T / ( √56 √61)
   •   =   (12+16+18)/( √56 √61)   =   46 / ( √56 √61)   =   0.78704
5. The angle is:
   • cos θ =  0.78704
   • θ =  arc cos 0.78704  = 38.1°

Not too far off from my guess.