Find the equation for the plane passing through the heads of the three given vectors
(2, 2, 0)
(−1, 2, 1)
(1, 1, 4)
If I was given 3 points, I know how to do this. Simply find AB x AC and plug one of the points into the equation to get a D value.
But given 3 vectors, I don't quite get it because when I take the cross of 2 of the given vectors I can't seem to find a D that works for all 3 points.
I am probably missing something simple.
The cross product technique you describe works to find a plane through the origin, but the plane you’re asked to find doesn’t do that. You can convert the problem into one that you can solve with this technique by translating back to the origin, solving, then translating back. I.e., pick one of the three vectors, subtract it from the other two, find the plane defined by these two new vectors and then add the one you subtracted back in.
