1. Chapter 2 Section 2.4 Lines and Planes in Space

2. x y z

3. A direction vector d for the line can be found by finding the vector from the first point to the second. To get a direction vector d that is perpendicular to both vectors u and v we can use the cross product.

4. This gives a system of equations with the variables t and u. Solve this system for t and u. This can be done in many ways here we equate the x and y components.

5. x y z To find a point on the line set the x -coordinate equal to 4 and solve for t. Plug that value into l to find the point. The direction vector l can be the normal vector N for the plane.

7. Example Find the equation of the line of intersection between the two planes whose equations are given to the right.