Section 12.5: Lines & Planes

If a, b, and c are not all 0, show that the equation \(ax + by + cz + d = 0\) represents a plane and \(\langle a, b, c \rangle\) is a normal vector to the plane. Hint: Suppose \(a \ne 0\) and rewrite the equation in the form \(a(x + d/a) + b(y - 0) + c(z - 0) = 0\)