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Intersection of a line and a plane

Statement. Line r passes through A(0, 6, 10) and B(12, 6, -2). Plane P is horizontal at height 4 (z = 4). Find the intersection point I.

Step-by-step solution

  1. Because P is horizontal, its vertical projection P'' is a horizontal line at height 4.
  2. Where r'' crosses P'' you have the vertical projection I'' of the intersection point.
  3. Drop a perpendicular from I'' to r' to place I'.
  4. Check that I belongs to the line: its coordinates must satisfy the equation of r.

Result

I(6, 6, 4).

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