Name:_____________________ Student Number: _______

[8] 1. Find an equation of the line passing through P(-1,-1,3) and orthogonal to the plane .

The vector (-1,2,-1) is orthogonal to the given plane; so it is parallel to the wanted line. So, the equation of the requested line is (in point parallel form): .

[8] 2. Find the intersection between the line and the plane .

Substitute in the equation of the plane to get . Solve for t to get . Substitute back in to get x=-7, y=2, z=-8. The point of intersection is .

[8] 3. Use elementary operations to solve the following system.

What is exactly the solution set?

After adding twice the first equation to the second we get the following system:

The solution set has not changed. We now observe that the second equation has no solution; consequently the last system has no solution, and so the original system has no solution too. The solution set is the empty set.