Posted by Heather on Wednesday, January 16, 2013 at 11:21pm.
Let L be the line that passes through the points (0,1,6) and (0,3,2). Find the length of the projection of k=<0,0,1> on the line L.
I know how to do this if one part of the vector k is touching the line, but unless i'm mistaken, that is not the case in this question. Your help is very much appreciated!

Calculus 3  Reiny, Thursday, January 17, 2013 at 12:12am
A vector in the direction of the line is (4, 2, 0)
so let u = (0,0,1) and v = (4,2,0)
just like before, the projection of u on v = u.v/v
= (0+0+0)/√20 = 0
of course the vector (0,0,1) is perpendicular to vector (4,2,0), so there is no projection
think of "projection" as the shadow that one line casts on the other line, and the above makes sense.
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