The Chemistry Maths Book, Second Edition

(Grace) #1

648 Solutions to exercises











  1. (i)


(ii) (iii)


Section 18.6



  1. (i)


(iii) and (vi) A


− 1

1 = 1 A


T

1 = 1 A


Section 18.7



  1. (i)E 1 = 1 identity


A 1 = 1 180°about Oz-axis


B 1 = 1 180°about Ox-axis


C 1 = 1 180°about Oy-axis


(ii)


EABC(applied first)


EEABC


AAECB


BBCEA


CCBAE






Chapter 19


Section 19.1










1


2


651


682


231


1


2


3



−−



























,


1


14


1


4


3


2


1


− 2



















,


BC


10


01


10


− 01



















EA


10


01


10


01




















AA



==















1

10 0


0


0


T

cos sin


sin cos


θθ


θθ


1


4


53


1


2















3

2

1

4

3

4

1

2

3

4

3

4

3

2

1

2

0



−−


−−
















cos cos sin sin sin


sin cos cos sin cos


φφφ


φφφ


θθ


θθ




0 −−−














sinθθcos


710118


0112 −










4664


1122














Section 19.2


























10.− 1 (double), (one vector only)






Section 19.3














  1. (i)




(ii)
′′=














x


3

12


12


1


xx


23

1


1


0


1


0


1


′′=−














=















,


1


2


1


0


1


1


2


1


2


1


1


2


1


2


− 1


























,,−
















1


3


1


1


1


0


0


1


1


3


1


1


1






























,,










1


2


1


1


1


2


1


− 1


















,


1


0


0


1


















,


0


1


2


2


1


1


32


,−















;,








cc (double) a











(all )a


c


1


− 1










0


1


0


1


32


1


2


1


, 32















;,














cc;− ,, −














c


1


2


1


−, −














;,














1 ;,


1


1


1


1


0


0


1


ccc 3


11


1


1














2


1


1


4


1


1


,











;,










cc


3


1


3


1
























ic


i


ic


i


,;,


2


1


0


3


0


1


,










;−,










cc


1


2


1


4


1


1


,











;,










cc


1


3


12 11


1121


2111


1112


1


2


3


1






















,
















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