Question

Find an equation for the plane that passes through the point [1, 1, 8] and that has [-1, -6, 3] as normal vector.

Answer 1

The normal to the plane is (Fx, Fy, Fz) = (1, 1, 8)
We have (x0, y0, z0) = (-1, - 6, 3)

Equation of the plane:
Fx(x - x0) + Fy(y - y0) + Fz(z - z0) = 0
=> (1)(x + 1) + (1)(y + 6) + (8)(z - 3) = 0
=> x + 1 + y + 6 + 8z - 24 = 0
=> x + y + 8z = 17