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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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