PHYS 301 HOMEWORK #1 Due : 29 Jan. 2010 Note : This homework and all future homeworks this semester must adhere to the following format specifications : •Your name must be on the first page of the assignment •Write only on one side of each sheet. •Pages must be stapled (not paper - clipped, edges folded over, etc.) in the upper left hand corner. I will lower by 10 % the grade of any homework not submitted according to these specifications. Homework solutions must show clearly the logic and steps you use to achieve your final result. No credit will be given to answers, even correct ones, lacking these solutions. Question #1 Find the angle between the vectors (2, 4, -3) and (-1, 3, 4) Question #2 Find the cross product of the two vectors described in question #1. Question #3 The two vectors defined in question #1 define a plane. Find the unit normal to the plane defined by these vectors. Question #4 Consider two vectors A and B and the angle q between them (see figure below). Use the properties of vectors and of the dot product to prove the law of cosines: c2 = a2 + b2 - 2 ab cos q where a, b, and c are the lengths of the vectors A, B, and C. 2 phys301-2010.hw1.nb C B q A Question #5 Consider the vectors p = (1, 2, -3); q = (2,-4,1); r = (3,-1,-3). Use Mathematica to compute the values of: p · (q â r) q·(râp) r·(q âp) Print out your Mathematica output and submit it along with the rest of your homework. (Do not use Mathematica, except to verify answers, for questions 1-4).