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: 14) Show: a) (AB)^{t} = B^{t}A^{t} 17) 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? 117) Obtain the cosine law of plane trigonometry by interpreting the dot product (AB)·(AB), and the expansion of this product. 123) Use the LeviCivita e_{ijk} notation to derive the vector identity: (A x B) x (C x D) = (ABD)C  (ABC)Dwhere ABC is defined to be the product (A x B)·C = (B x C)·A = (C x A)·B 124) 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?


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