Answer:
4x -4y +z = -7
Explanation:
The direction vector will be perpendicular to any/all vectors between the given points. It can be found, for example, using the cross product:
d = (P0Q0) × (P0R0) = (-3, -1, 8) × (-4, -3, 4)
The cross product can be computed by hand or by any of a number of calculators or web tools. Here it will be ...
d = (20, -20, 5)
These can be the coefficients of x, y, and z in the plane equation. However, the equation is better written using coefficients that are mutually prime, so we choose the direction vector to be ...
d = (4, -4, 1)
The constant C in the plane equation
d·(x, y, z) = C
will be the dot product of this direction vector (d) any any of the given points. Using R0, we find the constant to be ...
C = (4, -4, 1)·(0, 2, 1) = 4·0 +(-4)·2 +1·1 = -8+1 = -7
so, the plane equation is ...
4x -4y +z = -7