coordinate system represented by 0 may be found 
by applying vector analysis to the two matrices of the direction 
cosines and equating the angle between each pair of corresponding 
vectors. 
The angle between AB and AC should be the same in both 
system. Thus: 
(1) 
Obviously, 
M, = (2) 
The sign of M, is determined by taking the scalar product of 
two unit vectors in the direction of AB and AC in both systems. 
Furthermore, the angle between AP and AB should be the 
same in both systems. Thus: 
B5 Ps * 
b; ut mS t nn, 
Equating the angle between AP and AC in both systems, 
we get: 
Anl; + mm, + nn, =L..L 
25 2 3 2 3 2° 3 
M,