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)|)`

If `veca,vecb and vecc` are three non-coplannar vectors, then prove th

1.	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)\|)`
Answer» 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.

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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)|)`

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