Let O be an interior point of `Delta ABC` such that `2vec OA+5vec OB+10 vecOC=vec 0`

Let O be an interior points of triangleABC such that vec(OA)+2vec(OB)+3vec(OC)=vec0 , then the ratio of triangleABC to area of triangleAOC is

Let O be an interior point of triangle ABC, such that 2vec(OA)+3vec(OB)+4vec(OC)=0 , then the ratio of the area of DeltaABC to the area of DeltaAOC is

Let O be an interior point of triangle ABC, such that 2vec(OA)+3vec(OB)+4vec(OC)=0 , then the ratio of the area of DeltaABC to the area of DeltaAOC is

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

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

ABCD is a quadrilateral and O is point in its plabe such that vec OA+vec OB+vec OC+vec OD=0 show that 0 is the pooint of intersection of the lines joining the mid points of the opposite sides of quadrilateral ABCD.

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

If O and H be the circumcentre and orthocentre respectively of triangle ABC, prove that vec OA+ vec OB+ vec OC= vec OH .

ABCD is a quadrilateral and O is point in its plane. Show that if vec OA+ vec OB+ vec OC+ vec OD= vec 0 , then O is the point of the interection of the lines joining the mid-points of the opposite sides of ABCD.