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# Distance between 2 skew lines Watch

1. The question asks you to find the distance between two skew lines given their parametric equations:

L1: x=5+3k, y=-1-4k, z=1

L2: x=1+t, y=1+2t, z=1-2t

So I started by finding the direction vectors for each line which are L1: [3,-4,0] and for L2: [1,2,-2]. Then since the minimum distance between the 2 is perpendicular to both direction vectors, I found the cross product between the DVs and that was [8,6,10]... I'm not sure where to go from here and I am quite confused, please help
2. Find a point on each line, any will do. Find the vector between these 2 points.
Now find the component of this vector ("drop it onto..") which lies along your perpendicular found above using (a.b)/|b| where a is the vector joining the two points and b is the perpendicular vector.
Note, you can simplify the perpedicular vector should you chose.
Bric

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Updated: April 8, 2013
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