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Let ABC be a triangle and P be a point...

Let ABC be a triangle and P be a point inside ABC such that ` vec(PA) + 2vec(PB) + 3vec(PC) = vec0`. The ratio of the area of triangle ABC to that of APC is - (A) ` 2` (B) ` 3/2`(C) `5/3` (D) `3`

A

`2`

B

`3/2`

C

`5/3`

D

`3`

Text Solution

Verified by Experts

The correct Answer is:
D

`vec(PA) + 2vec(PB) + 3vec(PC) = 0`
`(veca - vecp) + 2(vecb- vecp) + 3(vecc - vecp) = 0`
`vecp = (veca + 2vecb + 3vecc)/(6)`
`("Area"DeltaABC)/( "Area" DeltaAPC) = (1/2|vecaxxvecb+vecbxxvecc+veccxxveca|)/(1/2|vecaxxvecp+vecpxxvecc+veccxxveca|)`
put `vecp = (veca+2vecb+3vecc)/(6)`
ratio `= 3`
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