Q:-If p=λ(u×v)+μ(v×w)+κ(w×u) and [uvw]=1/5,then find λ+μ+κ.(here p,u,v,w are vectors and λ,μ,κ are scalars)

Dear Tapasranjan Das

p=λ(u×v)+μ(v×w)+κ(w×u)

then

u.P =μ u.(vXw)

       =μ [u v w]

        =μ/5

similerly

  v.P = κ/5

and  w.P = λ/5

 add these value   (λ+μ+κ)/5 =u.P + v.P + w.P

                                 λ+μ+κ   =5(u+v+w).P

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