Using vector method in a triangle , prove that,
(i) `a/(sinA)=b/(sinB)=c/(sinC)` and

Explanation

According to Fig .2.59, `veca+vecc=vecb`
(i)`vecaxxvecb=vecaxx(veca+vecc)=vecaxxvecc " "[because vecaxxveca=0]`
`therefore |vecaxxvecb|=|vecaxxvecc|`
or, ab sin C =ac sin `theta`
(where `theta` is the angle between `veca and vecc` )
or, b sin C =c sin (`180^@-B)`
or, sin C =c sin B or, `b/(sin B) =c/(sin C)`
Proceeding in the same way, we get
`a/(sin A)=b/(sin B)=c/(sin C)`