You will have actual numbers in real equations, greatly simplifying the look of these equations. Using a point with two 0 values makes your work easier: x = 0 = y, which gives you:Ĭ 2 z 1 + d 2 - d 2 2 = 0 - d 2 (subtract d 2 from both sides)Ĭ 2 z 1 c 2 = - d 2 c 2 (divide both sides by c 2)ĭo not get hung up on the variables in our generic example. In our generic problem, we are using the second plane. Step 4: Pick a point ( x 1, y 1, z 1) on the other plane. Simply look at one equation and pull those coefficients, realizing a 1 is a (if you use the first plane), b 1 is b, and so on. Step 3: Identify coefficients a, b, c, and d in one of the plane equations. The two planes are parallel if their ratios are equal: Compare the ratios of each plane's three identified points ( a 1 a 2, b 1 b 2, c 1 c 2). Step 2: Are they intersecting or parallel? Remember, if they are parallel, your work is done! The distance is 0. Step 1: Write the equations for the planes in standard format, a x + b y + c z + d = 0, with subscripts indicating the two planes, 1 and 2, in our generic equations: Having previewed the steps, let's go through them.

Substitute for a, b, c, d, x1, y1 and z1 into the distance formula.

Find a point (x1, y1, z1) in the other plane.

Identify the coefficients a, b, c, and d from one plane equation.

Write equations in standard format for both planes.

Steps To Find The Distance Between Two Planes Part of your detective work is finding out if two planes are parallel. If they intersect, then at that line of intersection, they have no distance - 0 distance - between them. Think about that if the planes are not parallel, they must intersect, eventually. The distance between two parallel planes is understood to be the shortest distance between their surfaces.

Finding The Distance Between Two Planes.

Steps To Find The Distance Between Two Planes.

You could find the distance between those two planes mathematically. If you could imagine those two walls extending infinitely in their two directions (width and length not height), you would have two planes of a given distance apart. That means two walls in a room are probably parallel to each other.

The walls of your classroom, school or home are probably vertical to the floors and ceilings.

Finding distance in 3d spacie