⚡ Line of Intersection of Two Planes Calculator
Find the line of intersection between two planes
Plane 1: a₁x + b₁y + c₁z + d₁ = 0
Plane 2: a₂x + b₂y + c₂z + d₂ = 0
How to Use This Calculator
Enter Plane 1 Equation
Input coefficients a₁, b₁, c₁, d₁ for the first plane equation a₁x + b₁y + c₁z + d₁ = 0.
Enter Plane 2 Equation
Input coefficients a₂, b₂, c₂, d₂ for the second plane equation a₂x + b₂y + c₂z + d₂ = 0.
Calculate
Press "Find Intersection Line" to get the parametric equation of the intersection line.
Formula
Direction vector: d = n₁ × n₂
where n₁ and n₂ are normal vectors of the planes
Parametric form: r(t) = p + td
About Line of Intersection of Two Planes Calculator
The Line of Intersection of Two Planes Calculator finds the line where two planes intersect in 3D space. The direction vector is the cross product of the planes' normal vectors.
When to Use This Calculator
- 3D Geometry: Find intersection lines of planes
- Engineering: Calculate intersections in 3D designs
- Mathematics: Solve 3D geometry problems
Frequently Asked Questions
How do I find the line of intersection of two planes?
The direction vector is the cross product of the planes' normal vectors: d = n₁ × n₂. Then find a point on the line by solving the system of two plane equations. The line is given in parametric form: r(t) = p + td.
What if planes are parallel?
If the normal vectors are parallel (or proportional), the planes are parallel and have no intersection line. The calculator will indicate this.