MTH 310 Chapter Notes - Chapter 10_3: Dot Product

• School: University of Miami
• Department: Mathematics
• Course: MTH 310
• Professor: Benjamin Gammage

Document Summary

Dotproduct thedotproductla b oftwovectorsresultsas arealnumbernotavectorandiscalculatedasbelow a la asas b b b b ab ab a b ta b alsoholdsfortwodimensionalvectors sometimescalledthescalarproductorinnerproduct. Ex1 findthedotproduct ofthe vectorsbelow thedotproductfollowsmany ofthe laws ofordinaryproductsofrealnumbers propertiesofthedotproduct. 41ica b crab a rob go a 0. Theorem istheanglebtwnvectors a andbthen if a b tallblcos0 istheanglebtwnvectors a andbthen corollary if cosa a b tallbl. Ibl 25 947 538 a b 2s t 2 3t coson a. by. 23538 cos f 1. 46 l 2 to 6 2 2 twononzerovectorsare perpendicular ororthogonal if 0 12 twovectorsa and b are orthogonal iff a b 0. Ex4showthat li t2j k is l to si 4j 2k. 2i 2jk isi yj 2k to 8 2 0 theyare i samegeneraldirection. L wecanthink of a b asmeasuringtheextentat whicha and b pointinthesamedirection a b so a b o a b o a b tallbl. Ex5findthescalarandvectorprojectionofb cii 2 ontoa l2,3d try compab 9 projab faith a fy f 2,3 d.