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).`

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

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

If G is the centroid of a triangle ABC, prove that vec(GA)+vec(GB)+vec(GC)=vec(0) .

In a triangle ABC, if D and E are mid points of sides AB and AC respectively. Show that vecBE+ vecDC=(3)/(2)vecBC .

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) .

(Apollonius theorem): If D is the midpoint of the side BC of a triangle ABC, then show by vector method that |vec(AB)|^(2) + |vec(AC)|^(2) = 2(|vec(AD)|^(2)+ |vec(BD)|^(2)).

Let D ,Ea n dF be the middle points of the sides B C ,C Aa n dA B , respectively of a triangle A B Cdot Then prove that vec A D+ vec B E+ vec C F= vec0 .

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

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) .

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