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Physics 235: Classical Mechanics
Prof. S. Teitel stte@pas.rochester.edu ----- Fall 2001

## Problem Set 1

Due Thursday September 13 -- each problem below is worth 10 points

Do the following problems from Chapter 1 of the text:

4, 7, 17, 23, 24

For those who do not have a text, the problems are as follows:

1-4) Show:

a) (AB)t = BtAt
b) (AB)-1 = B-1A-1

1-7) Consider a unit cube with one corner at the origin and three adjacent sides lying along the three axes of a rectangular coordinate system. Find the vectors describing the diagonals of the cube. What is the angle between any pair of diagonals?

1-17) Obtain the cosine law of plane trigonometry by interpreting the dot product (A-B)·(A-B), and the expansion of this product.

1-23) Use the Levi-Civita  eijk notation to derive the vector identity:

(A x B) x (C x D) = (ABD)C - (ABC)D
where ABC is defined to be the product (A x BC = (B x CA = (C x AB

1-24) Let A be an arbitrary vector, and let e be a unit vector in some fixed direction. Show that:

A = e(A·e) + e x (A x e)
What is the geometrical significance of each of the two terms of the expansion?

Last update: Tuesday, August 14, 2007 at 7:31:37 PM.