What are the equations of the coordinate planes?

Explanation of Method

The equations of the three coordinate planes.

Step 1: Solution

Each coordinate plane contains two axes and is perpendicular to the third, whose unit vector is its normal. Each passes through $O$, so $D=0$ (Problem 183).

Plane	Contains	Normal	Equation
$xOy$	$Ox,\ Oy$	$\vec k$	$z=0$
$yOz$	$Oy,\ Oz$	$\vec i$	$x=0$
$xOz$	$Ox,\ Oz$	$\vec j$	$y=0$

$z=0$ $x=0$ $y=0$

The coordinate planes $xOy:\ z=0$, $yOz:\ x=0$, $xOz:\ y=0$.

Result

\[xOy:\ z=0,\qquad yOz:\ x=0,\qquad xOz:\ y=0\]