Applied Multivariate Techniques

Acquisitions Editors Tim Kent and Petra Sellers Assistant Editor Ellen Ford Marketing Manager Le!>lie Hines Production Editor Jennifer Knapp Cover and Text Design Harry Nolan CO\ er Pholognlph Telegraph Coluur Libr.lT)/FPG Intem:nional Corp. Mlmufacturing Manager Mark Cirillo Illustration Coordinator Edward Starr Outside Production Manager J. Carey Publishing Service This book was set in 10112 Times Roman by Publication Service!> and printed and bound by Courier St.)ughton. The cover was pnnlcd by Lehigh Press. Recognizing the importance of preserving what has been written. it is a policy of John Wiley & Sons. Inc. to have books of t'nduring "alue published in l~e l;nited States printed on acid-free paper. and we exert our best effom to that end. Copyright ~·1996 by John Wiley & Sons. Inc. All rights reserved. Published simuhancously in Canada. Reproduction or translation of any part or this work beyond that permitted h) Sections 107 and 108 of the 1976 United States Copyright Act without the permi~sion of the copyright owner is unlawful. Requests for pennission or funher information should be addre~sed to the Pennissions Depanment. John ~'iley & Son!.. Inc. LibrtlTJ of Congress Cataloging in PublicaJion [)ala: Shanna. Subhash. Applied multivariate techniques I Suhha~h Sharma. p. cm. Includes bibliogT3phical references. ISBN O-t71-31O repre5.enting the orthogonal axes EI and £.~. and f\ and f1 are oblique \,ecton; representing the oblique axes F 1 and F1. Vectors a and b are given as follows: a = O.500e 1 + 0.S66e1 b = 0.7oofl + 0.500f:!,. If the relationship between the orthogonal and oblique axes f\ = D.800el + 0.600e~ C: = D.70iel ~ D.70ie: i~ given by QUESTIONS 35 represem a with respect to f[ and f:! and b with respect to e. and f2. What is the angle between a and b? 2.7 Two cars stan from a stadium after a football game. Car A travels east at an average speed of 50 miles per hour while car B travels nonheast at an average speed of 55 miles per hour. What is the distance (euclidean) between the two cars after 1 hour and 45 minutes? 2.8 Cities A and B are separated by a 2.5-miIe-",ide river. Tom wants to swim across from a point X in city A to a point Y in city B that is directly across from point X. If the speed of the current in the river is 15 miles per hour (flowing from Tom's right to his left), in what direction should Tom swim from X to reach Yin 1 hour (indicate direction as an angle from the straight line connecting X and Y). 2.9 A spaceship Enterprise from planet Earth meets a spaceship Bakh-ra from planet Kling-on, in outer space. The instruments on Bakh-ra have ceased working because of a malfunction. Bakh-ra's captain requests the captain of Enterprise to help her determine her position. Enterpriu's instruments indicate that its position is (0.5,2). The instruments use the Sun as the origin of an orthogonal system of axes, and measure distance in light years. The Kling-on inhabitants, however, use an oblique system of axes (with the Sun as the origin). Enterprise's computers indicate that the relation between the two systems of axes is given by: k. = 0.810e 1 + 0.586e:z k2 = 0.732e[ + 0.681ez where the k; 's and ei 's are the basis vectors used by the inhabitants of Kling-on and Earth respectively. As captain of the Enterprise how would you communicate Bakh-ra's position to its captain using their system of axes? According to Earth scientists (who use an onhogonal system of a:l(es). Kling-on's poSition with respect to the Sun is (2.5,3.2) (units in light years) and Earth's positi