(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

ok so the problem is to evaluate (triple integral)x^2 dV of the solid tetrahedron with vertices (0,0,0) (1,0,0) (0,1,0) and (1,0,1)

2. Relevant equations

3. The attempt at a solution

so (triple integral)x^2 dzdydx

i made the x-y plane be the base with 0<x<1 and 0<y<1-x

for the z limits, i know they should be 0 to the plane but i am having trouble getting the equation of the plane. i need to use the points (1,0,0) (0,1,0) and (1,0,1) right?

but when i do the cross products of the two vectors <-1,1,0> and <0,0,-1> i get that the k component is 0. which makes no sense looking at the picture because z is not always zero. what am i doing wrong?

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# Homework Help: Equation of the plane, keep getting z=0 but can't be

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