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Question

Prove by the vector method, the law of sine in trignometry:
sinAa=sinBb=sinCc
628420_d14425865074415a9ba50242082778fc.png

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Solution

Let a,b,c be the sides of DABC then,
a+b+c=o......(1)
a×(a+b+c)=a×o
or a×a+a×b+a×c=o
a×b=c×a.....(2)
or b×a+b×b+b×c=0
or a×b=b×c.....(3)
By equation (2) and (3)
a×b=b×c=c×a
a×b=b×c=|c×a|
absin(pC)=bcsin(pA)=casin(pB)
sinAa=sinBb=sinCc
asinA=bsinB=csinC

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