Distance between two parallel lines in parametric form?

smci

New member
Give me the method to this question, and state the correct formula (preferably using same notation as I used):
http://answers.yahoo.com/question/index?qid=20101101232109AAnQbES
Go read that link and my answer, before you try to answer this.

Calculate distance between following parallel lines:
r = a+bs = (3 ,1, 2) + s (1, 1, 3)
r = c+dn = (1 , 0, 1) +n (1, 1, 3)
with a=(3,1,2), c=(1,0,1), b=d=(1,1,3)

Was I not correct to say
(slant) displacement vector (e) between the two lines is: e = (a-c) = (2,1,1)
Orthogonal length of e wrt to d=(1,1,3), by projection of e onto d, and then subtraction:
D = | e - (e.d / d.d) d |
which by my calculation would give ?186 / 5
 
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