Prove that the lines and intersect each other and find the point of their intersection.
Given: The equations of the two lines are and
To Prove: The two lines intersect and to find their point of intersection.
Formula Used: Equation of a line is
Cartesian form: .
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.