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

The four points A = (-1, -1, -1), B = (1, 1, -1), C = (1, -1, 1) and D = (-1, 1, 1) are the vertices of a triangular pyramid. Use vectors to calculate:

d) an equation (in vector form) of the plane parallel to the face ABC and containing the point D

3. The attempt at a solution

I have to admit that I'm at a bit of a loss here. The equation of the plane is given by ax+by+cz=s. If the plane is parallel, then it contains the points A, B, and C.

So would I use the cross product of the vectors ACxAB = ai + bj + ck

Then plug in a, b and c for the equation of the plane, while using the point D for x, y and z, getting:

a(x+1) + b(y-1) + c(z-1) = 0

Working this out, I get:

AB = <2, 2, 0>

AC = <2, 0, 2>

ACxAB= -4i + 4j + 4k

-4(x+1) + 4(y-1) + 4(z - 1) = 0

-4x +4y + 4z = 12

-x + y + z = 3

Any help figuring out if I'm on the right track is greatly appreciated :)

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# Homework Help: 3D Vector Problem

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