I have these set of points: (0,0,0) , (1,0,0) , (0,2,0) , (0,0,3)

this is a tetrahedron.

I have absolutely NO idea how to make an equation from points in the form of

x+y+z = ?

any help on this would be great on a general form of how to do this.

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- Apr 25th 2010, 06:42 PMRET80making equations from points in R3
I have these set of points: (0,0,0) , (1,0,0) , (0,2,0) , (0,0,3)

this is a tetrahedron.

I have absolutely NO idea how to make an equation from points in the form of

x+y+z = ?

any help on this would be great on a general form of how to do this. - Apr 25th 2010, 08:57 PMmr fantastic
- Apr 26th 2010, 02:36 AMHallsofIvy
There is NO single equation to describe a tetrahedron. You appear to be talking about an equation for the plane that includes (1, 0, 0), (0, 2, 0), (0, 0, 3). You probably have already learned that you can construct two vectors in the plane by using those points, say <0-1, 2-0, 0-0>= <-1, 2, 0> AND <0-1, 0- 0, 3- 0>= <-1, 0, 3>, then use the cross product to find a vector perpendicular to the plane. Once you have that, the plane with perpendicular vector <A, B, C> containing point $\displaystyle (x_0, y_0, z_0)$ has equation $\displaystyle A(x- x_0)+ B(y- y_0)+ C(z- z_0)= 0$.

For this simple situation, you can also use the fact that any plane (that does not pass through the origin) can be written as Ax+ By+ Cz= 1. Put the three given points in for x, y, and z to get three equations to solve for A, B, and C.