Subject: RE: CCL:Geometry question, send again if not solved

From: Daquan Gao <[email-masked]>
Date: Tue, 20 Jul 1999 08:34:11 -0500

Since there is some interest in the question, I will post my solution. I
suppose this is the same as the original question.

The original question: Given 3 points, A(a1, a2, a3), B(b1,b2,b3) and
C(c1,c2, c3), find the coordinate of a fourth point (or atom) D(x,y,z)
 provided with the following 3 conditions:
   	distance BD,
        angle ABD,
        angle ACD.
 
I propose the following recipe, 

(1) Find distances, AD and CD based upon
the angle and distance of the related triangles. 

(2) Using the angle and
distances in triangle ABD, set up an equation: (a1-b1)(x-b1) +
(a2-b2)(y-b2)+ (a3-b3)(z-b3)= AB. BD.cos(ABD). Similarly, set two other
equations like this one. 

(3) Solve the 3 linear equations for x, y, and z.

Besides, there is a more standard procedure than this, namely DISTANCE
GEOMETRY method. It is not really necessary for this problem.

Sincerly,

Daquan Gao