Puttiing the cosine of a direction cosine in terms of Cartesian coordinates

Re: Puttiing the cosine of a direction cosine in terms of Cartesian coordinates

Quote:

Originally Posted by

**topsquark** Here's the problem for what it is worth.

Bear with me and I'll get to the Trigonometry part.

The dipole moment is defined as

(The

is the displacement vector from the origin to the point where the charge q sits.)

Now pick a point

in three space. Specifically

The dipole term of the potential is calculated by

where

is the direction cosine of the angle between

and

. (ie. the cosine of the angle between

and the y axis, if we make the triangle form by putting the tails of

and

at the origin.)

The question then is how to write

in terms of Cartesian coordinates? I could use the Law of Cosines to find the angle if I had the length of the line between the heads of

and

. I could use the Law of Sines, but I don't have any of the angles in the triangle.

Any thoughts? Thanks!

-Dan

(sobs) It was right in front of me the whole time!

Ah well. Thanks anyway!

-Dan