I want to transform from rectangular coordinates ( xyz) to (x",y",z") rectangular coordinates that is rotated at the origin as show in the attachment. Then I want to transform (x",y",z") rectangular coordinates into Spherical coordinates. Attach is the method I use, I want to verify I am doing it correctly. Basically I want to transform the xyz into any position on the SAME ORIGIN as shown in Fig.1. I first rotate along z axis on the xy plane as shown in Fig.2. I rotate clockwise as shown by angle ##\alpha##. I called the new coordinates as (x',y',z') as intermediate coordinates. Then the second step is to rotate along x' axis as shown in Fig. 3 by angle ##\beta## to get the final (x",y",z") coordinates. I also show my work step by step in the drawing attached. [PLAIN]http://i43.tinypic.com/2uxwt52.jpg[/PLAIN] Then the final step of transforming to Spherical coordinates is by the same method like [tex]\hat R=\hat x''(\hat x''\cdot \hat R)+\hat y''(\hat y''\cdot\hat R)+\hat z''(\hat z''\cdot\hat R)[/tex] Am I correct? Thanks a million.