Vector question

  1. can all vectors have projection on an arbitrary line? What if the vector and the line do not intersect and are not parallel (i.e. they cannot lie on the same plane).
     
  2. jcsd
  3. HallsofIvy

    HallsofIvy 40,542
    Staff Emeritus
    Science Advisor

    Yes, if you allow the zero vector as a projection. for example, a vector pointing along the x-axis has the 0 vector as its projection on the y-axis.

    For an example where "the vectors do not intersect and are not parallel" but lie along skew lines, consider a vector pointing along the x-axis and the line given by the parametric equations x= t, y= t, z= 1. The projection is again the 0 vector.
     
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