Chapter 12.5, Problem 83E

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

$a\left(x+\frac{d}{a}\right)+b\left(y-0\right)+c\left(z-0\right)=0$