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Question

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 AD+BD+CH+3HG=λHD, then what is the value of the scalar λ?

A
2
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B
3
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C
1
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D
2
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Solution

The correct option is A 2
We know that in vector
AB=OBOA where O is the origin
SO from ques
AD+BD+CH+3HG=λHD
ODOA+ODOB+OHOC+3OG3OH=λHD
2OD2OHOAOBOC+3OG=λHD
2(ODOH)OAOBOC+3OG=λHD
2HDOAOBOC+3OG=λHD
Comparing both sides
λ=2

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