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## Homework Statement

Let L

_{1}be the line (0,4,5) + <1,2,-1>t and L

_{2}be the line (-10,9,17) + <-11,3,1>t

a) Find the line L passing through and orthogonal to L

_{1}and L

_{2}

b) What is the distance between L

_{1}and L

_{2}

## The Attempt at a Solution

I only know how to do part of part a). I can only find the direction vector of the orthogonal line by taking the cross product. I have,

<1,2,-1> x <-11,3,1> = <5,10,25>, which I simplify to <1,2,5>.

It doesn't seem very obvious to me how I can find a point (presumably on either L

_{1}or L

_{2}) such that a line containing this point, pointing in the direction of <1,2,5>, passes through both L

_{1}and L

_{2}.

For part b), I presume that these two lines are skew. (How do you check if lines are parallel or intersect?) The distance between these two lines is

|<5,10,25> dot [(0,4,5) - (-10,9,17)]| = |<5,10,25> dot <10,-5,-12>| = |50 - 50 - 300| = 300. So the distance is 300?