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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