Plane Intercept Form (3D) Calculator

This Plane Intercept Form (3D) Calculator helps you write a plane in intercept form in three-dimensional space. Start with either a standard plane equation or the x-, y-, and z-intercepts, then rewrite the equation in the form x/a + y/b + z/c = 1. This makes it easier to see where the plane meets each axis. It is a simple way to check answers, understand the method clearly, and practise 3D coordinate geometry step by step.

Step-by-step method

1. Put the plane into standard form Ax + By + Cz = d.
2. Compute the intercepts a = d/A, b = d/B, c = d/C.
3. Write intercept form x/a + y/b + z/c = 1.

Formula:

Example 1: 2x+3y-4z=12

Step 1 - Put the plane into Ax + By + Cz = d and read off A, B, C, d.

In this problem: Rewrite your plane in standard form (if needed), then identify A, B, C and d.

Step 2 - Compute the intercepts.

In this problem: Use a = d/A, b = d/B, c = d/C.

Step 3 - Write intercept form.

In this problem: Substitute a, b, c into x/a + y/b + z/c = 1.

Final answer: x/a + y/b + z/c = 1 with a=6, b=4, c=-3

Example 2: (2,3,-4)

Step 1 - Identify the intercepts a, b, c.

In this problem: Read the x-, y-, z-intercepts from the input.

Step 2 - Write intercept form.

In this problem: Substitute a, b, c into x/a + y/b + z/c = 1.

Step 3 - Optional: write standard form.

In this problem: Multiply through to remove denominators.

Final answer: x/a + y/b + z/c = 1 with a=2, b=3, c=-4