1. Describe the coordinate system that you will use. Your coordinate system should be right-handed.
Where is the origin? How are the axes aligned? You may find it useful to include a sketch of the
coordinate system, but you should also give some description in sentences.
2. In your coordinate system, write down a vector representing the direction that the laser is pointing.
[Hint: if your answer cannot be multiplied by a scalar to eliminate all square roots, then look closer.]
3. Write down a vector equation for the line representing the laser beam as it leaves the laser.
4. At what point does the laser beam hit a mirrored wall?
5. The laser light reflects perfectly off the mirrored wall. Write down a vector representing the direction
that the laser beam points after reflection.
6. Now write down a vector equation for the line representing the reflected laser beam.
7. Find two vectors in the plane of the movable mirror and hence find a normal to the mirror. Regardless
of the location of this mirror, this will always be its normal.
8. You will need to place this mirror somewhere along the path of the reflected laser beam to reflect it one
more time. The beam reflects according to the description given above. Show that the formula in point
(B) obeys the physical laws in point (A). Then use the formula to write down a vector representing
the direction of the reflected laser beam.
9. Now write down an equation for the line representing the twice-reflected laser beam. This will have
two unknown parameters.
10. The laser beam should now be able to hit the steel cable. Write down a vector equation for the line
representing the steel cable and hence write down a system of three linear equations to solve so that
the laser beam hits the cable.
11. What is the point at which the laser beam hits the movable mirror (assuming you don’t want to free
the monster)?