Equation of a plane and distance from a point to that plane
Here's the problem:
"Consider the three points P = (1,7,3), Q = (5,9,2) and R = (2,6,5) that form a triangle.
a) Do these three points form the vertices of a triangle? If so, determine which point is the vertex of the right angle. (Use vector arithmetic and not the Pythagorean Theorem, to check if this is a right triangle.)
b) Find the equation of the plane that contains this triangle using a cross product calculation.
c) Find the distance from the point (2,2,0) to the plane that contains this triangle using a dot product calculation."
a) PQ = (4,2,-1) and PR = (1,-1,2)
There's no number t where PQ = PR, which means they're non-collinear and hence, a triangle.
PQ (dot) PR = 4-2-2 = 0, which means they're perpendicular at P, and so the right angle is also at P.
b) PQ x PR = [4,2,-1] x [1,-1,2] = 3i+9j-6k
I haven't gotten to part c yet, but does my work so far look good? Although, I did something wrong in part b, because the equation doesn't fit all the points, but I'm not sure what.