M 311                                           Spring 2004
                                                                                
                HOMEWORK SUMMARY REPORT
                                                                                
                                                                                
Chapter number: 1
                                                                                
Section number: 2
                                                                                
Exercise number: 14
                                                                                
Number of papers received: 2
                                                                                
Reviewing committee: epsilon
                                                                                
List all participating committee members:
    c-glaser, j-bosshard
                                                                                
Author(s) of paper(s) chosen for publication: 
 [James Macfarlane and reviewers' alternative]
                                                                          
                                                                                
Comments: James's proof is essentially correct, while [the other] made a
logical error by setting theta equal to zero. However, we believe an
alternate solution presented below more closely follows the spirit of
vector calculus:
                                                                                
If r represents the displacement vector from the origin to any arbitrary
point in the plane, and n is any vector normal to the plane, then r dotted
with the unit normal vector (n/|n|) is the scalar projection of r onto the
unit normal vector, which is the distance from the origin to the plane.  
Since it is stated that |n| = 1, by simplification, r dot n is the
distance from the origin to the plane.  And by Theorem 2, r dot n is d.  
Thus, d is the distance from the origin to the plane.

INSTRUCTOR'S COMMENT: I think that James's trig-based argument is also 
worth displaying.