What is the relationship of the given line L: (x,y,z) = (-2,1,5) + t<2,-8,-6> to each of the lines below? Is it coincident, parallel, intersecting or skew? 5. (-1,-3,2) + t<-3,12,9>

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to check if the lines are parallel, hence, you need to test if the direction vectors of the lines are scalar multiples of each other.

`<2,-8,-6> = k*<-3,12,9> => {(2 = -3k),(-8 = 12k),(-6 = 9k):}`

`{(k = -2/3),(k = -8/12),(k = -6/9):}`

Reducing duplicate factors yields:

`{(k = -2/3),(k = -2/3),(k = -2/3):}`

You may notice that `<2,-8,-6>` and `<-3,12,9>` are scalar multiples of each other, hence, the lines areĀ  parallel.