Plane P1 (Blue)
Equation: ax + by + cz = d
Plane P2 (Red)
Equation: ax + by + cz = d
Understanding how two planes intersect is a fundamental concept in 3D geometry and vector mathematics. This interactive tool makes it simple: just enter the
equations of any two planes, and it will automatically calculate their line of intersection step by step.
We use the cross product of the planes' normal vectors to find the direction vector of the intersection line, then set
z=0 in the equations of the planes and solve for \( x \) and \( y \) to find a point on the line of intersection. Every stage of the calculation is clearly shown.
The result is displayed visually in a 3D coordinate system, where you can see both planes and their intersection line (highlighted in yellow), and you can interact with using the mouse and its wheel to rotate and zoom.
Equation: ax + by + cz = d
Equation: ax + by + cz = d
Enter the coefficients for both planes and click "Calculate & Visualize" to see the line equation and 3D visualization.