Find the point of intersection and the cosine of the angle of intersection.

Question

Determine whether the lines intersect, and if so, find the point of intersection and the cosine of the angle of intersection.

Answer 1

Step 1:

The line equations are and .

Let the line L₁ be equated to t and solve for x, y and z.

Let the line L₂ be equated to s and solve for x, y and z.

Now equate the corresponding x, y and z values.

                   Equation (1)

                   Equation (2)

           Equation (3)

Step 2:

Subtract equation (2) from equation (3).

Substitute in equation (2).

Substitute in the line equation L₁.

Substitute in the line equation L₁.

The two points are not equal, hence the lines are not intersecting lines.

Solution:

The two lines do not intersect.