Show that the lines and do not intersect each other.
Given: The equations of the two lines are and
To Prove: the lines do not intersect each other.
Formula Used: Equation of a line is
where is a point on the line and is the direction ratios of the line.
So a point on the first line is
A point on the second line is
If they intersect they should have a common point.
Solving (1) and (2),
Substituting for the z coordinate, we get
So, the lines do not intersect.