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Let O be an interior point of `DeltaABC` such that `bar(OA)+2bar(OB) + 3bar(OC) = 0`. Then the ratio of a `DeltaABC` to area of `DeltaAOC` is

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The correct Answer is:
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`bar(OA)+bar(2OB)+bar(3OC)=vec(0)`………i
Let `x,y, z` be the area of triangle `OAB, OBC` and `OCA` respectively and area `(DeltaABC)=A`
`impliesx+y+z=A`………..ii
Taking cross product with `bar(OA)` on the both sides i and then take modulus on both sides, we get `x/y=3/2impliesx=3/2y`
similarly `x/z=3` and `y/z=2impliesz=y/2`
`:.` from ii `y(3/2+1+1/2)=AimpliesA/y=3`
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