Show that the lines and intersect each other. Also, find the point of their intersection.

Show that the lines and intersect each other. Also, find the point of their intersection.
Answer
Given: The equations of the two lines are and
Io Prove: The two lines intersect and to find their point of intersection.
Formula Used: Equation of a line is
Vector form:
Cartesian form:
where is a point on the line and is the direction ratios of the line.
Proof:
Let
So a point on the first line is
A point on the second line is
If they intersect they should have a common point.

Therefore,
Substituting for the coordinate, we get
and
So, the lines intersect and their point of intersection is