Let G be the centroid of the DeltaABC, whose sides are of lengths a,b,c. If P be a point in the plane of triangleABC, such that PA=1,PB=3, PC=4 and PG=2, then the value of a^(2)+b^(2)+c^(2) is

Let G be the centroid of the DeltaABC, whose sides are of lengths a,b,

1.	Let G be the centroid of the DeltaABC, whose sides are of lengths a,b,c. If P be a point in the plane of triangleABC, such that PA=1,PB=3, PC=4 and PG=2, then the value of a^(2)+b^(2)+c^(2) is
Answer» 42 40 36 28 Solution :As `\|veca+vecb+VECC\|^(2)+ \|veca-vecb\|^(2)+\|vecb-vecc\|^(2)+\|vecc-veca\|^(2)` `=3(\|veca\|^(2)+\|vecb\|^(2)+\|vecc\|^(2))` So, `9(GP)^(2)+(AB)^(2)+(BC)^(2)+(CA)^(2)` `=3(PA)^(2)+(PB)^(2)+(PC)^(2)` `RARR 9 xx 2^(2)(a^(2)+b^(2)+c^(2))=3(1^(2)+3^(2)+4^(2))` `rArr a^(2)+b^(2)+c^(2)=42`

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Let G be the centroid of the DeltaABC, whose sides are of lengths a,b,c. If P be a point in the plane of triangleABC, such that PA=1,PB=3, PC=4 and PG=2, then the value of a^(2)+b^(2)+c^(2) is

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