
Inclination of axis
have 3 mutually perpendicular axis X' , Y' and Z'
Line AB lies on X' and I know the global coordinates of A and B [that is coordinates cooresonding to axis X, Y and Z
I want to find:
1. Inclination of X' with global X , Y and Z axis.
2. Inclination of Y' with global X , Y and Z axis.
3. Inclination of Z' with global X , Y and Z axis.
Please helpvery very urgent!!!

We found a reference wherein the author follows the approach below to determine the directional cosines :
l1 , m1, n1 which are the cosines of the angles between x' axis and the global x, y and z axis
l2 , m2, n2 which are the cosines of the angles between y' axis and the global x, y and z axis
l3 , m3, n3 which are the cosines of the angles between z' axis and the global x, y and z axis
However, we have not understtod the appraoch.I will describe below what he has done.
l1 , m1 and n1 is clear; that is;
l1 = x2  x1 / length (AB)
m1 = y2  y1 / length (AB)
n1 = z2  z1 / length (AB)
Let
Vx' be a matrix such that
[Vx' ] = [l1 m1 n1]^T
Then, he takes a reference point C such that C does not lie along the line joining AB
Let the coordinates of C be (x3,y3,z3)
He then gets:
"V13" where V13 is a matrix
V13 = [ (x3  x1) / l13 (y3  x1) / l13 (z3  x1) / l13]
where,
l13 is the distance between A and the reference point.
Now,
[l3 m3 n3] ^T = (Vx ' x V13) / modulus of (Vx ' x V13)
Let:
[l3 m3 n3] ^T = Vz'
Note: (Vx ' x V13) denotes cross product
Next:
[l2 m2 n2] ^T = Vz' x Vx'
Note: (Vz ' x Vx') denotes cross product
We do not follow the approach above?
He has not given any explanation for above.
Whatever, he has given we have described above???