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