
#1
Nov1711, 11:33 PM

P: 127

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
Nov1811, 07:42 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,879

Yes, if you allow the zero vector as a projection. for example, a vector pointing along the xaxis has the 0 vector as its projection on the yaxis.
For an example where "the vectors do not intersect and are not parallel" but lie along skew lines, consider a vector pointing along the xaxis 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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