If `veca,vecb and vecc` are three non-coplannar vectors, then prove that `(|hataxx(hatbxxhatc)|)/sinA=(|hatbxx(hatcxxhata)|)/sinB=(|hatcxx(hataxxhatb)|)/sin C = (prod|hata xx(hatbxx hatc)|)/(|sum sinalpha cosbeta cosgamma hatn_(1)|)`

Explanation

Since `veca,vecb and vecc` are non - coplanar, vectors `vecaxxvecb,vecb xxveccandveccxxveca` are also non-coplanar. Let
`vecd=l(vecbxxvecc)+vecm(veccxxveca)+vecn(vecaxxvecb)`
now multiplying both sides of (i) scalarly by `veca` we have
`veca.vecd=lveca.(vecbxxvecc)+mveca.(veccxxveca)+nveca.(vecaxxvecb)=l[vecavecc veca]([veca vecc veca]=0=[veca veca vecb])`
`l=(veca.vecd)//[veca vecb vecc]`
putting these values oif l,nm and n and (i) , we get the required relation.