Physics 235: Classical Mechanics Problem Set 1Due 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:
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:
1-24) Let A be an arbitrary vector, and let e be a unit vector in some fixed direction. Show that:
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