Plane Intercept Form (3D) Calculator
This Plane Intercept Form (3D) Calculator rewrites a plane so that the three numbers in it are the points where it crosses the axes, and shows the working line by line. Dividing the whole equation by the constant term is what turns each coefficient into an intercept. A zero coefficient means the plane runs parallel to that axis and never crosses it. Following the same pattern every time keeps each intercept tied to its own axis.
Step-by-step method
- Set up the problem.
- Compute the intercepts a = d/A, b = d/B, c = d/C.
- Write intercept form x/a + y/b + z/c = 1.
See Example 1 Hide Example 1
Problem
Approach
Step-by-step method
- Set up the problem.
- Compute the intercepts a = d/A, b = d/B, c = d/C.
- Write intercept form x/a + y/b + z/c = 1.
Step 1
Step 1 - Set up the problem.
In this problem: The plane in standard form is \(2x + 3y + 4z = 12\).
Step 2
Step 2 - Write the intercept form.
In this problem: Each denominator is where the plane crosses that axis.
Step 3
Step 3 - Compute the intercepts a = d/A, b = d/B, c = d/C.
In this problem: The intercepts are \(6\), \(4\), and \(3\).
Step 4
Step 4 - Write intercept form x/a + y/b + z/c = 1.
In this problem: Divide the standard form by d.
Final Answer
See Example 2 Hide Example 2
Problem
Approach
Step-by-step method
- Set up the problem.
- Compute the intercepts a = d/A, b = d/B, c = d/C.
- Write intercept form x/a + y/b + z/c = 1.
Step 1
Step 1 - Set up the problem.
In this problem: The plane in standard form is \(x - 2y + 5z = 10\).
Step 2
Step 2 - Write the intercept form.
In this problem: Each denominator is where the plane crosses that axis.
Step 3
Step 3 - Compute the intercepts a = d/A, b = d/B, c = d/C.
In this problem: The intercepts are \(10\), \(-5\), and \(2\).
Step 4
Step 4 - Write intercept form x/a + y/b + z/c = 1.
In this problem: Divide the standard form by d.
Final Answer
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Example Problems
Click one to load it into the box and solve it.