Line–plane intersection

You cannot simply “see” where a line pierces a plane on the drawing – both have views, but the piercing point does not fall out of them directly. Hence the cutting-plane method.

The idea is simple: through the line p we pass a helper plane – usually a projecting plane perpendicular to π₁, because then its plan collapses onto p₁. This covering plane cuts the given plane ρ in a line m.

Now p and m lie in one plane, so they meet – and their intersection R is both on p and in ρ. That is exactly the piercing point. Check: R₁ must lie on p₁, R₂ on p₂, and both on a shared ordinate.