# Solid angles and position vectors

1. Jun 7, 2007

### Mattew

Hi everybody, I'm gonna post my problem in this section even if It could me posted in physics, too.
I'm using solid angles to define directions of objects moving from the centre of the sphere towards all points in the space around, which means I divides the (4pi) solid space around the centre in K-> infinity directions, each one defined by a solid angle w(i). It is a procedure commonly used in 2D, where each object departing from the centre of a disk chooses its direction in [0, 2pi]...the only difference appears to be the magnitude of the entire space, which is 4pi (solid angle of the sphere) in this case.
Now my problem is: If I have two position vectors defininig two of the objects movements in directions w1 and w2, how do I find the angle between them whithout introducing further coordinates (polar or x,y,z axis?). Is there a possibility to find the relative direction (each one defined by a soli angle) of the two vectors based on the only w parameter?
In 2D, calling teta1 and teta2 (in [0,2pi]) the directions of the two objects, i would graphically represent them on a x-y cartesian system and find the angle between them as teta2 - teta1, so the sum vector of the two would be sqrt[(v1cos(teta2-teta1))^2 + v2^2 sin(teta2 - teta1)^2 ], but I can't figure out how it works im my 3D framework.
Can anybody give me some hints?
Thanks