(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine if any of the lines are parallel or identical

L1 (x-8)/4 = (y+5)/-2 = (z+9)/3

L2 (x+7)/2 = (y-4)/1 = (z+6)/5

L3 (x+4)/-8 = (y-1)/4 = (z+18)/-6

L4 (x-2)/-2 = (y+3)/1 = (z-4)/1.5

2. Relevant equations

L1 pt(8,-5,-9) V<4,-2,3>

L2 pt(-7,4,-6) V<2,1,5>

L3 pt(-4,1,-18) V<-8,4,-6>

L4 pt(2,-3,4) V<-2,1,1.5>

3. The attempt at a solution

I know that if the vectors are scalar multiples, they are either parallel or identical. What I don't know, is after I find out that V(L3) = -2*V(L1). How do I determine if they are parallel or identical. I assume that since one vectors k value is 1.5, it is some multiple of another line, if not they wouldn't have given a 1.X. So L1 L3 L4 are parallel but how could I find if they were identical or not?

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# Homework Help: Parametric equations and lines

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