Prove that `3vec(OD)+vec(DA)+vec(DB)+vec(DC)` is equal to `vec(OA)+vec(OB)+vec(OC)`.

if A,B,C,D and E are five coplanar points, then vec(DA) + vec( DB) + vec(DC ) + vec( AE) + vec( BE) + vec( CE) is equal to :

ABCDE is a pentagon. Prove that the resultant of forces vec (AB), vec(AE), vec(BC), vec(DC), vec(ED) and vec(AC) is 3vec(AC) .

Statement 1 : In DeltaABC , vec(AB) + vec(BC) + vec(CA) = 0 Statement 2 : If vec(OA) = veca, vec(OB) = vecb , then vec(AB) = veca + vecb

Let vec(a), vec(b), vec(c) be vectors of length 3, 4, 5 respectively. Let vec(a) be perpendicular to vec(b)+vec(c), vec(b) to vec(c)+vec(a) and vec(c) to vec(a)+vec(b) . Then |vec(a)+vec(b)+vec(c)| is :

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)=

ABCDEF is a regular hexagon. Show that : vec(OA)+vec(OB)+vec(OC)+vec(OD)+vec(OE)+vec(OF)=vec0 . Where O is the centre of the hexagon.

Prove that [vec a+ vec b, vec b +vec c, vec c + vec a]= 2 [vec a vec b vec c]

If vec(a).vec(b)=0 and vec(a) xx vec(b)=0, " prove that " vec(a)= vec(0) or vec(b)=vec(0) .

D,E,F are mid-points of the sides of the triangle ABC, show that for any point O, the system of concurrent forces represented by vec(OA),vec(OB),vec(OC) is equivalent to the system represented by vec(OD),vec(OE),vec(OF) .

In pentagon ABCDE, prove that : vec(AB)+vec(BC)+vec(CD)+vec(DE)+vec(EA)=vec0 .