Parametric equations and lines

Brigada
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Homework Statement


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

Homework 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>

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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After careful consideration, and pulling my head out of the book to think logically, I realized after I find the parallel lines, if a point I chose that satisfies one equation, also satisfies another line equation, they are identical, if its not on the line, it's still parallel, just not identical. That was 1.5 hours wasted on a brain fart!
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
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