# Expressing a vector with respect to another vectors origin

1. Sep 4, 2012

### ejay_hi

1. The problem statement, all variables and given/known data
Given that A_vec = 3*r_hat - 7*theta_hat + 2*phi_hat w/ origin at (1, pi/2, 0 (deg))
and B_vec = -2*r_hat - 4*theta_hat + 2*phi_hat w/ origin at (3, pi/2, pi/2).

The vectors are represented in Spherical Coordinates.

Determine A - B with respect to A, and with respect to B.

2. Relevant equations

I do not know how to represent a vector with respect to another vector's origin. I do however, know how to take the difference when they are both originate at the same point:

A - B = (Ar - Br)*r_hat + (Atheta - Btheta)*theta_hat + (Aphi - Bphi)*phi_hat

3. The attempt at a solution

To solve for A' (A with respect to B's origin) I tried:
Origins of A_vect: (a0, a1, a2)
Origins of B_vect: (b0, b1, b2)

A' = (Ar - (b0 - a0))*r_hat +(Atheta - sin(b1-a1))*theta_hat + (Aphi - cos(b1-a1))*phi_hat

However, I do believe that this is wrong. Can someone help point me to the correct way of thinking about this problem.