If `AD, BE and CF` be the median of a `/_\ABC`, prove that `vec(AD)+vec(BE)+vec(CF)`=0

If AD, BE and CF are the medians of a Delta ABC, then evaluate (AD^(2)+BE^(2)+CF^(2)): (BC^(2) +CA^(2) +AB^(2)).

If O is the circumcentre and P the orthocentre of Delta ABC , prove that vec(OA)+ vec(OB) + vec(OC) =vec(OP) .

If G is the centroid of /_\ABC, prove that vec(GA)+vec(GB)+vec(GC) =0. Further if G_1 bet eh centroid of another /_\PQR , show that vec(AP)+vec(BQ)+vec(CR)=3vec(GG_1)

Prove that vec i xx(vecjxxveck)=vec0

If O is the circumcentre, G is the centroid and O' is orthocentre or triangle ABC then prove that: vec(OA) +vec(OB)+vec(OC)=vec(OO')

If ABCDEF is a regular hexagon, prove that vec(AC)+vec(AD)+vec(EA)+vec(FA)=3vec(AB)

AD is a median of triangle ABC. Prove that : AB+AC gt 2AD

In a regular hexagon ABCDEF, prove that vec(AB)+vec(AC)+vec(AD)+vec(AE)+vec(AF)=3vec(AD)

If A,B,C,D are any four points in space prove that vec(AB)xxvec(CD)+vec(BC)xvec(AD)+vec(CA)xxvec(BD)=2vec(AB)xxvec(CA)

If D,E and F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC and lambda is scalar, such that vec(AD) + 2/3vec(BE)+1/3vec(CF)=lambdavec(AC) , then lambda is equal to