Orthocenter of an equilateral triangle ABC is the origin O. If `vec(OA)=veca, vec(OB)=vecb, vec(OC)=vecc`, then `vec(AB)+2vec(BC)+3vec(CA)=`

In a triangle OAC, if B is the mid point of side AC and vec(OA)=veca,vec(OB)=vecb , then what is vec(OC) .

If O( vec0 ) is the circumcentre and O' the orthocentre of a triangle ABC, then prove that i. vec(OA)+vec(OB)+vec(OC)=vec(OO') ii. vec(O'A)+vec(O'B)+vec(O'C)=2vec(O'O) iii. vec(AO')+vec(O'B)+vec(O'C)=2 vec(AO)=vec(AP) where AP is the diameter through A of the circumcircle.

In triangle ABC, find vec(AB)+vec(BC)+vec(CA)

OAB is a given triangle such that vec(OA)=vec(a), vec(OB)=vec(b) . Also C is a point on vec(AB) such that vec(AB)=2vec(BC) . What is vec(AC) equal to ?

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)

Let O be the centre of the regular hexagon ABCDEF then find vec(OA)+vec(OB)+vec(OD)+vec(OC)+vec(OE)+vec(OF)