Symmetric equations of the lines are and .

Standard form of symmetric equations of the line are .

Here vector is parallel line to the above line.

Parallel line corresponding to the line is .

Consider .

Similarly parallel line corresponding to the line is .

Consider  .

If these two parallel lines are parallel, then the lines and also parallel.

Find the cross product of and .

The cross product is not equal to zero, then the lines are not parallel.

Check for intersection of the  lines:

If and had a point of intersection, find the point by solving the lines.

Consider and

Write the line equations in parametric form.

and .

Equate the corresponding values.

Solve equations and to find the values of and .

Multiply the equation by .

Subtract the above two equations.

Substitute in .

substitute and in .

Thus, the values of   satisfy .

The lines and are intersecting lines.

Substitute these   in the line equation to get the point of intersection.

.

.

.

The point of inter section is .

The lines and are intersecting lines.

The point of intersection is .