# Equation of tetrahedron

• Nov 18th 2012, 07:19 AM
mrmaaza123
Equation of tetrahedron
What will be the equation of the tetrahedron that passes through the points (0,0,0),(1,0,0),(0,1,0) and (0,0,1) ?

help will be appreciated.
• Nov 18th 2012, 10:20 AM
topsquark
Re: Equation of tetrahedron
Quote:

Originally Posted by mrmaaza123
What will be the equation of the tetrahedron that passes through the points (0,0,0),(1,0,0),(0,1,0) and (0,0,1) ?

help will be appreciated.

I don't understand. A tetrahedron doesn't have an "equation."

-Dan
• Nov 18th 2012, 07:06 PM
mrmaaza123
Re: Equation of tetrahedron
Well basically i have to evaluate a triple integral xyz over a region D which is a tetrahedron with the vertices (0,0,0),(1,0,0),(0,1,0) and (0,0,1). So basically i need the equation of the plane that will pass through these points. Maybe i wrote it in the wrong way. Will it be x+y+z=1 or x-y+z=1 ?

My professor used the latter one to solve the integral i can't figure out why?
• Nov 19th 2012, 12:12 AM
hollywood
Re: Equation of tetrahedron
I was just working with tetrahedrons and similar objects. You can actually define a tetrahedron as the subset of $\mathbb{R}^4$ with $x,y,z,w\ge{0}$ and $x+y+z+w=1$, a definition that generalizes easily to any number of dimensions.

But looking at your problem, for the point (0,1,0), x-y+z is -1, so that doesn't work. Based on what you said, x+y+z=1 is the correct equation. If you can post the exact problem and the professor's solution, maybe we can figure out what happened.

Since you're setting up a triple integral, you will want limits of integration, which will look like:
$\int_0^1{\int_0^{1-z}{\int_0^{1-y-z} xyz\ dx\ dy\ dz}}$
depending on what order you choose to integrate over x, y, and z.

- Hollywood
• Nov 19th 2012, 12:36 AM
mrmaaza123
Re: Equation of tetrahedron
Thank you so much! This was actually blowing my mind up! I think my professor messed it up a little.