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 Exercise [11.02] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [11.02]
q_{1}=t_{1}+u_{1}i+v_{1}j+w_{1}k
q_{2}=t_{2}+u_{2}i+v_{2}j+w_{2}k
Define the operations as follows:
Addition:
q_{1}+q_{2}=t_{1}+t_{2}+(u_{1}+u_{2})i+(v_{1}+v_{2})j+(w_{1}+w_{2})k
Multiplication:
q_{1}q_{2}
=t_{1}t_{2}-u_{1}u_{2}-v_{1}v_{2}-w_{1}w_{2}
+(t_{1}u_{2}+u_{1}t_{2}+v_{1}w_{2}-w_{1}v_{2})i
+(t_{1}v_{2}+v_{1}t_{2}-u_{1}w_{2}+w_{1}u_{2})j
+(t_{1}w_{2}+w_{1}t_{2}+u_{1}v_{2}-v_{1}u_{2})k
(This formula arises when you multiply out q_{1}q_{2} and follow the identities ii=jj=kk=-1, i=jk,j=ki,k=ij ,ij=-ji,jk=-kj and ki=-ik assuming the distributive law)


26 May 2008, 10:07
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