i came across a question today about the distannce between two parallel lines in 2D and i was wondering
if i am asked the distance between two parallel lines, could i find the distance between the two parallel planes that these vectors were on in 3D (if the z component was equal to 0 for both planes)?
Personally, what I would do is choose an arbitrary point on one of the lines, construct the plane perpendicular to the line through that point (very simple since you are given the line and so a vector perpendicular to the plane), determine where the other line intersected the line, then find the distance between those two points.
ok so that is equal to 14/((58)^(1/2)) but if i use x.n=-4 and x.n=10 where n = <3,4,0> then i get |-4-10|/((9+49)^(1/2)) which is equal to the same thing,
so i was wondering if treated parallel lines as planes parallel to the z-plane if i can use this to find the distance?