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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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Answer» Solution :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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