1.

Let ABC be a triangle whose centroid is G, orhtocentre is H and circumcentre is the origin 'O'. If D is any point in the plane of the triangle such that no three of O, A, C and D are collinear satisfying the relation vec(AD) + vec(BD) + vec(CH ) + 3 vec(HG)= lamda vec(HD), then what is the value of the scalar 'lamda'?

Answer»


SOLUTION :L.H.S = ` vecd - veca + vecd - vecb + vech - vecc + 3 (vecg - vech)`
`"" = 2 vecd - ( veca + vecb + vecc) + 3 (( veca + vecb + vecc))/(3) - 2 vech`
`"" =2 vecd - 2 vech = 2(vecd - vech) =2 VEC(HD)`
`RARR lamda =2 `


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