Question

Can anyone tell me that if two lines in 3 space intersect, how do we find that? And the logic behind it? (Trying to work on concepts)

Answer 1

method 1
if the lines lie on the same plane then they will intersect if they are no paallel
method 2
fine the common point of intersection if any for the ines

Answer 2

assume any point on line 1 to be of the form
as lr1+x1,mr1+y1, nr1+z1
and that on the second line be lr2+x2,mr2+y2, nr2+z2
for the lines to intersect
the equations lr1+x1=lr2+x2
mr1+y1=mr2+y2 and nr1+z1=nr2+z2
after solving unique values of r1 and r2
and the point of intersection of the lines can be found out