# Bonus question for exam 1 (up to +10% of your... score) G. Berkolaiko September 14, 2009

```Bonus question for exam 1 (up to +10% of your exam
score)
G. Berkolaiko
September 14, 2009
From Wikipedia: “Specular reflection” follows the law of reflection, which states that
the incoming direction and the outgoing direction make the same angle with the surface
normal. Both directions and the normal lie in the same plane.
Part I (+5% of your exam score): A point-like object traveling in the direction
~v = hxv , yv , zv i undergoes a specular reflection off a plane with the equation ax+by +cz = d.
Find a formula for the reflected direction ~u.
Part II (+5% of your exam score): You are trying to sink a billiard ball located at
the point A(5, 1, 1) into a hole located at the point B(0, 3, −6) by reflecting the ball off the
plane x + 2y − z = 0. Find the point on the plane that you must aim for to sink the ball.
Rules:
1. You must not copy the solution from any source (such as Internet or a book). You
must not seek outside help on this problem. Doing so is plagiarism and therefore
cheating.
2. If you choose to collaborate on this project, you must acknowledge your collaboration and the resulting bonus (if any) will be split evenly among the collaborators.
3. Not acknowledging your collaboration is cheating and will not be tolerated.
4. Cheating is contrary to the values of academic integrity at Texas A&amp;M University and
to the Aggie Honor. Punishment for cheating is severe: http://aggiehonor.tamu.edu/Student
Rules/sanctions.html
1
```