I've already posted this question in the math section, but since I got no reply I'll try it here (sorry for the cross-posting).(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Solid angles and position vectors

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