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Let O be an interior points of triangleA...

Let O be an interior points of `triangleABC` such that `vec(OA)+vec(OB)+3vecOC=vec0`, then the ratio of `triangleABC` to area of `triangleAOC` is

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The correct Answer is:
3
`("Area of" triangleABC)/("Area of" triangleAOC)= (1/2|vecaxxvecb+vecbxxvecc+veccxxveca|)/(1/2 |veca xxvecb|)`
now `veca + 2vecb + 3vecc = vec0`
Cross multiply with `vecb, vecaxxvecb +3vecc xxvecb=vec0`
`Rightarrow vecaxxvecb= (vecb xxvecc)`
`vecaxxvecb = 3/2(veccxxveca) = 3(vecb xxvecc)`
`Let (vecc xxveca)= vecp`
`veca xxvecb = (3vecp)/2, vecbxxvecc= vecp/2`
`Ratio = (|vecaxxvecb=vecb xxvecc +vecc xxveca|)/(|veccxxveca|)`
`(|(3vecp)/2 + vecP/2 +vecp|)/(|vecp|)`
`(3|vecp|)/|vecp|=3`
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