Line of Intersection of Two Planes Calculator

Your details

Coefficient of x in the first plane equation ax + by + cz = d.
Coefficient of y in the first plane equation.
Coefficient of z in the first plane equation.
Right-hand side constant of the first plane equation.
Coefficient of x in the second plane equation ax + by + cz = d.
Coefficient of y in the second plane equation.
Coefficient of z in the second plane equation.
Right-hand side constant of the second plane equation.
Status
Intersecting

Whether the planes are parallel, identical, or intersecting.

Direction vector - x component-5
Direction vector - y component2
Direction vector - z component-4
Point on line - x0
Point on line - y1
Point on line - z-1
x(t)x(t) = -5t
y(t)y(t) = 1 + 2t
z(t)z(t) = -1 - 4t
Angle between planes19.45deg
Direction vector magnitude6.7082
Direction x-5
Direction y2
Direction z-4

The two planes intersect in a straight line.

  • The direction vector of the intersection line is r = <-5, 2, -4>, found as the cross product of the two normal vectors.
  • A specific point on the line is P0 = (0, 1, -1). You can verify this by substituting it into both plane equations.
  • The dihedral angle between the two planes is 19.45 degrees.
  • Any scalar multiple of the direction vector is also valid: the line extends infinitely in both directions.

Next stepUse the parametric equations x(t), y(t), z(t) to trace the entire intersection line by varying the parameter t.

 = Powered by OnlyCalculators