Unit 1ProjectionsHARD

Angle Between Two Lines

Two lines AB and AC intersect at A. AB: A(20,25,30), B(60,50,15). AC: A(20,25,30), C(55,10,50). Find the true angle between them.

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Solution Diagram

Solution diagram for Angle Between Two Lines
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Step-by-Step Construction

  1. 1

    Draw projections of both lines from common point A

  2. 2

    To find true angle, both lines must show their true lengths simultaneously

  3. 3

    This occurs in a view parallel to plane containing both lines

  4. 4

    First, draw auxiliary view parallel to one line to make it a point

  5. 5

    Then draw second auxiliary view to show both lines in true length

  6. 6

    Measure the angle in this view - this is the true angle

  7. 7

    Alternatively, use vector method: cos θ = (AB·AC)/(|AB||AC|)

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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