Plane vector rotation How do I compute the x,y,z rotations in degrees to move a plane with a normal vector of 0,0,1 (rotate it) so that its normal vector has a new position of 0.508, 0.699, 0.502?  
Essentially, I need to move a plane from one location/orientation to another, about the x, y, z axes.  The staring and ending positions of the normal vector this plane are known (noted above). 
 A: You create a tranformation matrix.  You have decribed what we will do to (0,0,1)
But what will we do to $(1,0,0)$ and $(0,1,0)?$  
There is not a unique transformation that takes $(0,0,1)$ to $(0.508, 0.699, 0.502)$
To keep the transformation rigid (one the preserves angle measures and distances) we will need to find unit vectors that are orthogonal to $(0.508, 0.699, 0.502)$
$(-0.699, 0.508,0)$ will be orthogonal to $(0.508, 0.699, 0.502)$
If we divide the vector by its norm, (i.e. $\sqrt {0.699^2 + 0.508^2}$ we will have one ortho-normal vector.
And if we take the cross product of these two vectors we will get a third ortho-normal vector.
$\pmatrix {0.295 & -0.809 & 0.508\\0.406&0.588&0.699\\-0.864&0&0.502}\pmatrix{x\\y\\z}$
Will rotate any point and rotate $(0,0,1)$ to the desired location.
A: Do you mean a plane with a normal vector of (0,0,1) rotates so that the normal vector has a new position of (0.508, 0.699, 0.502)?
In this case, the new normal vector (0.508, 0.699, 0.502) show the directional cosines $(\theta_x,\theta_y,\theta_z)$, so your requests are $\frac{180}{\pi}(\arccos(0.508),\arccos(0.699),\arccos(0.502))$.
Hope it helps...
