Question

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.

Answer 1

Step 1:

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 are also parallel.

Find the cross product of and .

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

 

Answer 2

Continued:

Step 2:

Check for intersection of the  lines:

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

Consider and

Write the line equations in parametric form.

and .

Equate the corresponding values.

             Equation(1)

       Equation(2)

   Equation(3)

Solve equation(1) and equation(2) and find the values of and .

Multiply the equation(1) by 2.

Subtract the above two equations.

Substitute in equation(1).

substitute and in equation(3).

Thus, the values of   satisfy the equation(3).

The lines and are intersecting lines.

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

The point of inter section is .

Solution:

The lines and are intersecting lines.

The point of intersection is .