1. What is the Intersection of Two Planes?

The intersection of two planes in three-dimensional space is typically a straight line. This occurs when the planes are not parallel and not coincident.

2. How Does the Calculator Work?

The calculator solves the system of equations representing the two planes:

Where:

• \( plane1 \) — First plane equation (e.g., Ax + By + Cz = D)
• \( plane2 \) — Second plane equation (e.g., Ex + Fy + Gz = H)

Explanation: The calculator finds the parametric or symmetric equations of the line where the two planes intersect.

3. Importance of Plane Intersection

Details: Understanding plane intersections is crucial in 3D geometry, computer graphics, engineering design, and physics simulations.

4. Using the Calculator

Tips: Enter both plane equations in standard form (Ax + By + Cz = D). The calculator will determine their line of intersection if one exists.

5. Frequently Asked Questions (FAQ)

Q1: What if the planes don't intersect?
A: The calculator will indicate if the planes are parallel (no intersection) or coincident (infinite solutions).

Q2: What format should I use for plane equations?
A: Use standard form (e.g., 2x - 3y + z = 5) with variables x, y, z.

Q3: Can I use different variable names?
A: The calculator currently only supports x, y, z as variables.

Q4: How is the line of intersection represented?
A: Typically as parametric equations or symmetric equations.

Q5: What if my planes are in different forms?
A: Convert them to standard form (Ax + By + Cz = D) before entering.