Two Planes

This calculator finds the angle between two planes, determines their relative position and calculates the distance between parallel planes.

cos φ = ^{|A₁A₂ + B₁B₂ + C₁C₂|}/_{√(A₁² + B₁² + C₁²) · √(A₂² + B₂² + C₂²)}

For parallel planes with the same normal the distance is |D₁ − D₂| / √(A² + B² + C²).

Example. x + 2y + 2z − 3 = 0 and 2x + 4y + 4z + 5 = 0 are parallel. Dividing the second equation by 2 gives D₂′ = 2.5. The distance is |−3 − 2.5| / 3 ≈ 1.83.