# Math Help - tetrahedra

1. ## tetrahedra

Hi friends ……….

If u all can plz help to solve this problem….
The problem goes as follows……

There is an irregular tetrahedron ABCD . the length AB BC AC AD BD CD that is the length of the 6 edges of the tetrahedron are known. The coordinates of one of the faces say ABC is known . let the coordinates be A(x1 y1 z1) B(x2 y2 z2) and C(x3 y3 z3) . with these given data I want to determine the coordinates of the fourth point that is D.

If any one can suggest an analytical approach to solve this problem with these given datas

2. Originally Posted by bibhudutta mishra
Hi friends ……….

If u all can plz help to solve this problem….
The problem goes as follows……

There is an irregular tetrahedron ABCD . the length AB BC AC AD BD CD that is the length of the 6 edges of the tetrahedron are known. The coordinates of one of the faces say ABC is known . let the coordinates be A(x1 y1 z1) B(x2 y2 z2) and C(x3 y3 z3) . with these given data I want to determine the coordinates of the fourth point that is D.

If any one can suggest an analytical approach to solve this problem with these given datas
Use the distance formula:

Let D(d1, d2, d3) denote the top of the tetrahedron. |AD| is the (known!) length of the edge AD. Then you get a system of simultaneous equations :

$\sqrt{(a_1-d_1)^2+(d_2-a_2)^2+(d_3-a_3)^2}=|AD|$

Do the same with B and C.

Then solve the system for (d1, d2, d3). You should get 2 solutions with the plane ABC as the mirror plane.

3. thanks my dear..................

i am already using this distance formula

the three distance formula leads to three spheres ...............let the three spheres be C1 C2 C3..................C1-C2 and C1-C3 gives rise to two plane.....now these two planes intersect to form a line.................intersection of this line with the sphere C1 gives the two required points...........

this is the approach that i am following..............so if u can tell me if this approach is correct...............and at the same time suggest any alternate way of solving this problem....

4. Originally Posted by bibhudutta mishra
thanks my dear..................

i am already using this distance formula

the three distance formula leads to three spheres ...............let the three spheres be C1 C2 C3..................C1-C2 and C1-C3 gives rise to two plane.....now these two planes intersect to form a line.................intersection of this line with the sphere C1 gives the two required points...........

this is the approach that i am following..............so if u can tell me if this approach is correct...............and at the same time suggest any alternate way of solving this problem....
That's precisely the way I would have used myself with a slight extension:

1. Square the 3 distance equations to get rid of the square roots.

2. Calculate
C1 - C2
C1 - C3
C2 - C3
to get rid of the squared values

3. You now have a system of linear equations which you can solve for d1, d2, d3

By the way: It would be easier for me to explain the procedure if you can post an example

5. thanks again..............

but i cant produce a numerical example..............

bcoz this problem is part of a bigger modelling n simulation based program............so it has to be worked out with the every general conditions without any numerical example.................and then at each step of the solution conditions have to be checked and evaluated so that it fits into all kinds of cases..............i hope u r able 2 understand what i mean to say,......................

i think i am not evaluating each n every conditions properly after obtaining a general solution or in the process of obtaining the general solution for which my program is not running smoothly after a few iterations

6. Originally Posted by bibhudutta mishra
.........so it has to be worked out with the every general conditions without any numerical example.................and then at each step of the solution conditions have to be checked and evaluated so that it fits into all kinds of cases....
I tried to get a general solution but I only got back real monster terms without any practical use. Sorry, but I can't help you with your problem

7. anyways.......

thanks a lot.....