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.