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Solved descriptive geometry exercises

Step-by-step exercises from the Technical Drawing syllabus with the drawing already built. Each one opens in the 3D editor so you can rotate it, measure it and check the solution.

• Traces of a line — Lines
  Line r passes through points A(0, 6, 5) and B(12, 2, -3). Find its traces with the horizontal plane (H) and with the vertical plane (V).
• Intersection of a line and a plane — Intersections
  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.
• Distance from a point to a plane — Distances
  Find the distance from point P(3, 5, 7) to the horizontal plane z = 2.
• Line parallel to a plane through a point — Parallelism
  Through point P(2, 6, 6), draw a horizontal line parallel to plane P: x + y + z = 6.
• Rotation onto the horizontal plane — Rotations into the projection plane
  Point A(3, 4, 5) belongs to plane P: y = 4. Rotate the plane onto the horizontal plane and find the rotated position (A).
• Angle between two planes — Angles
  Find the angle between the horizontal plane z = 0 and plane Q: x + z = 0.
• Does the point belong to the line? — Lines
  Line r passes through A(0, 3, 0) and B(8, 3, 4). Check whether point P(4, 3, 2) belongs to r.
• Line perpendicular to a plane — Perpendicularity
  Through point P(2, 4, 6), draw the line perpendicular to plane P: y = 4.
• Intersection of two planes — Intersections
  Find the intersection line of planes P: z = 2 and Q: y = 3.
• True length by change of plane — True lengths
  Segment AB has A(0, 2, 2) and B(6, 5, 6). Find its true length with a change of plane.
• Rotation of a point around a vertical axis — Rotations
  Rotate point A(6, 4, 2) by 90 degrees around the vertical axis through the origin.
• PAU Madrid 2024-25 · Distance between parallel lines — Distances
  Lines r and s are parallel: r passes through A(0, 0, 6) and s through B(0, 5, 2), and both have direction (3, 4, 0). Find the true length of the distance between r and s. (Adaptation of the original statement: the exam gives the figure; the coordinates are fixed here so it can be built in the editor.)
• PAU Madrid 2025 · Angle between two lines — Angles
  Lines f and h meet at P(4, 4, 2). f has direction (1, 0, 1) and h direction (1, 1, 0). Find the angle they form and justify the construction. (Adaptation of the original statement: the exam gives the figure; the coordinates are fixed here so it can be built in the editor.)
• PAU Madrid 2024-25 · Net of the frustum — True lengths
  The pyramid has a square base, 4 units side and 6 units height. It is cut by a horizontal plane at mid-height (z = 0). Find the net of the resulting frustum. (Adaptation of the original statement: the exam gives the figure; the measurements are fixed here so it can be built in the editor.)

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