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Math 201 (section 3)
September 6, 2004
revised September 8, 2004 (adding 13.5, #1)
Read:
Section 13.3 (Dot products):
We'll use the term "component of b in the direction of a as a synonym for "scalar projection of b onto a." Skip the page on "direction cosines" if you like.)
Section 13.4 (Cross products):
Useful for angular momentum, magnetism, and finding certain areas and directions. Stop at the first mention of "physics" on page 855.)
Section 13.5 (Equations of planes and lines):
Read ahead for Friday and maybe next Monday.
Problems to turn in:
Section 13.3: 2, 6, 8, 10, 14, 22, 24. Also:
Problem B. What is the scalar projection of <-100, 600> onto <1, 1> ? (Hint: not 500.)
Problem C. A sailboat wants to go northeast, but must tack against the wind. On one leg it manages to go 100 yards west
and 500 yards north. How many yards progress (if any) has it made in the northeast direction ?
Problem D. What is the sum of the three answers you gave to problem 22 ?
Problem E. Can you find four different points P, Q, R, S in 3-space such that all of the distances PQ, PR, PS, QR, QS, RS are the same ?
Section 13.4: 4, 10, 13, 16, 23 (area of a two-dimensional parallelowhatchamacallit), 29 (volume of a three-dimensional parallelowhatchamacallit).
Section 13.5: Problem 1. Just say "true" or "false" on each; no explanations needed. "True" means always true.
(end)
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