Calculate projection of a line in a square

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Said that we have two points (P1, P2) that form a line, and 3 points (S1,S2,S3) that form a triangle, how would we calculate the position X and Y of the point resulting from the intersection of the line and the plane containing the triangle?

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in the 3D-coordinate system (x,y,z):

  • write the line that joins $p_1p_2$
  • find the point of this line with $z$-coordinate $=0$ (intersection with your plane)
  • done