If ABCD is a quadrilateral and E and F are the midpoints of AC and BD respectively, then prove that `vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(EF)`.

If A B C D is quadrilateral and Ea n dF are the mid-points of A Ca n dB D respectively, prove that vec A B+ vec A D + vec C B + vec C D =4 vec E Fdot

Let A, B, and C be the vertices of a triangle. Let D, E, and F be the midpoints of the sides BC, CA, and AB respectively. Show that vec(AD)+vec(BE)+vec(CF)=vec(0) .

If D is the midpoint of the side AB of a triagle ABC prove that vec(BC)+vec(AC)=-2vec(CD)

prove that [vec(a)-vec(b),vec(b)-vec(c)vec(c)-vec(a)]=0

If D is the midpoint of the side BC of a triangle ABC, prove that vec(AB)+vec(AC)=2vec(AD)

If D and E, are the midpoints of the sides AB and AC of a triangle ABC, prove that vec(BE) +vec(DC)=(3)/(2)vec(BC).

ABCD a parallelogram, and A_1 and B_1 are the midpoints of sides BC and CD, respectively. If vec(A A)_1 + vec(AB)_1 = lamda vec(AC) , then lamda is equal to

If ABCDE is a pentagon then prove that vec(AB)+vec(AE)+vec(BC)+vec(DC)+vec(ED)+vec(AC)=3vec(AC)

The value of vec(AB)+vec(BC)+vec(DA)+vec(CD) is