Let us recall how we determine the position of a point T that lies in the plane
P the point must lie on the straight line that belongs to this plane.
The construction of the intersection point P of a straight line
p with a plane P (assumed that
the line doesn't belong to that plane or is parallel to it and the plane is in
general position) is based on finding the line of the plane P that intersects the line p in the point of intersection of p and P .
To construct the point of intersection P of a straight line and a plane in
general position we
proceed as follows:

1. Σ , p ⊂ Σ 2. f = P ∩ Σ 3. P = p ∩ f = p ∩ P 
1. Intersection of a straight line and a plane using a plane in general position as auxiliary plane.
2. Intersection of a straight line and a plane using a projecting plane as auxiliary plane.
The comparison of the two given constructions are presented in the figures below. Because of the simplicity of the second approach we will always use projecting planes as auxiliary planes in the construction
Auxiliary plane Σ is an oblique plane. 
Auxiliary plane E is a projecting plane. 
Construction of the intersection of the line p with horizontal projecting plane Σ. 
Construction of the intersection of the line p with vertical projecting plane Σ. 
Created by Sonja Gorjanc, translated by Helena Halas and Iva Kodrnja  3DGeomTeh  Developing project of the University of Zagreb