Math 127(3) - Warren D. Smith - Homework #2 - due Tues 4 Feb 2003
------------------------------------------------------------------
Continue reading ch 12 (note the "chapter highlights" checklist page
836-837...) and start reading ch 13.

1. Do exercises 20, 32, 38, and 48 
of section 12.3, pages 803-804.

2. There is a plane pictured on the top left of page 834.
It goes thru the 3 points (006), (400) and (030).
Find the angle between this plane and the XY plane
(in degrees, do it accurate to 0.1 degree or better).

3. Compute   (1,5,7) X (6,2,3).

4. In section 12.7 pages 835-836 of the book,  they list 7 propositions
in geometry which they'd like you to prove by vector-algebra methods.
Choose one of them, and prove it.



---------

FOR THOSE WITHOUT BOOK... THESE ARE AGAIN:

20:  find angle (in radians and in degrees) between (-2,-3,0) and (-6,0,4)

32: when does |a.b| = |a|  |b|  ?   (here a,b are vectors.)

38:   If   a,b parallel and a,c parallel, show   a is parallel to pb+qc 
for any reals p,q.  (here a,b,c are vectors.)

The props in sec 12.7 are
2. If inscribe an angle in a semicircle, must be a right angle.
3. Sum of sqs of lengths of diagonals equals sum of sqs of lengths of
the sides of a parallelogram.
4. The 3 altitudes of a triangle meet at a point.
5. The 3 medians of a triangle meet at a point.
6. law of sines: sinA/|a| = sinB/|b| = sinC/|c|
7. two planes with a point in common have a line in common.
prove one of these by vector algebra methods.