Mathematics

Problem

Let

ABC

be a triangle whose centroid is

G

, orthocentre 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} = \lambda \vec{HD}

, then what is the value of the scalar '

\lambda