Now I have a spherical coordinate system whose origin is located at (a,b,c)[cartesian], and I have another point whose location is (r, theta, tho) in this spherical system, and P's cartesian coordinate is (x1,y1,z1).
Now if I want to make (0,0,0) as the new origin of another spherical coordinate system by moving each point as much as the origin does. The origin moved from (a,b,c) to (0,0,0), then point P will move from (x1,y1,z1) to (x1 - a, y1 - b, z1 - c). After all the move, will the spherical coordinate remain the same in the spherical system centered at (0,0,0), will it still be (r, theta, rho)?
It is like if I know the angle that the point have with the positive direction of z-axis, and the distance from the point to the origin and I know the angle of the projection of that point onto xy plane with the positive direction of x-axis, then no matter how i define the orthogonal basis, I can find the corresponding cartesian coordinate with a give origin. Is it correct?