Find equation of plane containing points: (1,1,5),(3,5,3),(8,8,1),(10,2,2),(18,6,-1),(-1,-3,6)
Find 2 vectors given 3 points, using a common point. The cross product of these 2 vectors will be the normal vector of the plane. Use normal vector coords <a,b,c> as coefficients in the ax+by+cz=d formula where x,y,z is any point in the plane and solve for d. This equation better be true for all points.
The Attempt at a Solution
P = (1,1,5)
Q = (3,5,3)
R = (8,8,1)
PQ = <2,4,-2>
PR = <7,7,-4>
PQ x PR = <-2,-6,14>
Plug in point P into formula and get:
-2x-6y+14z = 62
Test formula by plugging in Q and don't get 62.