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Let ABC be a triangle whose centroid is ...

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'`?

Text Solution

Verified by Experts

The correct Answer is:
2
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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