Let a, b, c ∈ R3.
a) Prove that if a, b, and c do not all lie on the same line, then an equation of the plane through these points is given by (x, y, z) • d = a • d, where
d := (a - b) × (a - c).
b) Prove that if c does not lie on the line ɸ(t) = ta + b, ∈ R, then an equation of the plane that contains this line and the point c is given by (x, y, z) • d = b • d, where d := a × (b - c).