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## Main Question or Discussion Point

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).

- Thread starter batballbat
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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

HallsofIvy

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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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