Unit 1ProjectionsHARD

Shortest Distance Between Two Skew Lines

Line1: A(10,15,20) to B(50,40,15). Line2: C(15,10,40) to D(45,35,25). Find the shortest distance between these non-intersecting lines.

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Solution Diagram

Solution diagram for Shortest Distance Between Two Skew Lines
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Step-by-Step Construction

  1. 1

    Draw projections of both lines in FV and TV

  2. 2

    Check if lines intersect - if not, they are skew lines

  3. 3

    Shortest distance is perpendicular to both lines simultaneously

  4. 4

    Draw auxiliary view showing one line as a point

  5. 5

    In this view, measure perpendicular distance to second line

  6. 6

    This is the shortest distance

  7. 7

    Vector method: d = |(B-A)·((C-A)×(D-C))| / |(D-C)×(B-A)|

Pro Tips

  • •Always verify your measurements with a scale before finalizing the drawing
  • •Use construction lines lightly and darken the final solution
  • •Label all important points and reference lines clearly

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