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1. Vector Analysis

1.1 SCALARS AND VECTORS

Scalar refers to a quantity whose value ay !e re"resente# !y a sin$le%"ositive or ne$ative& real nu!er.

A vector quantity has !oth a a$nitu#e1 an# a #irection in s"ace. 'e areconcerne# with two( an# three(#iensional s"aces only) !ut vectors ay !e#e*ne# in n(#iensional s"ace in ore a#vance# a""lications.

1.+ VECTOR AL,E-RA

Coutative law for a##ition

Associative law for a##ition

Associative law for scalar ulti"lication

Distri!utive law for scalar ulti"lication

Dot ro#uct

Cross ro#uct

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1./ T0E RECTAN,LAR COORD2NATES3STE4

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1./ T0E RECTAN,LAR COORD2NATES3STE4

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1.5 VECTOR CO4ONENTS AND N2TVECTORS

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De*ne a vector *el# an# scalar *el#

'e have #e*ne# a vector *el# as a vector functionof a "osition vector. 2n $eneral) the a$nitu#e an##irection of the function will chan$e as we ove throu$hout the re$ion) an# the value of the vector fun

ction ust !e #eterine# usin$ the coor#inate values of the "oint in question. -ecause we have consi#ere# only the rectan$ular coor#inate syste) we e6"ect the vector to !e a function of the varia!les x ,

y) an# z. 2f we a$ain re"resent the "osition vector as r) then

a vector *el# G can !e e6"resse# in functionalnotation as G%r&7 a scalar *el# T is written as T %r&.

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E6a"le of vector *el# an# scalar

*el#

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1.8 T0E DOT RODCT

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E6a"le 1.+

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1.9 T0E CROSS RODCT

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T0E DOT RODCT an# CROSSRODCT

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1.: C2RCLAR C3L2NDR2CALCOORD2NATES

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1.; T0E S0ER2CAL COORD2NATES3STE4