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

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

ABCD is a quadrilateral. If M and N are the mid points of the sides vec(BD) and vec(AC) , respectively. Show that vec(AB)+vec(AD)+vec(CB)+vec(CD)=4vec(NM)

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

Prove by vector method that in any triangle ABC, the point P being on the side vec(BC) , if vec(PQ) is the resultant of the vectors vec(AP) , vec(PB) and vec(PC) , then ABQC is a parallelogram.

If G is centroid of the triangle ABC, then find vec(GA)+vec(GB)+vec(GC).

If vec(a) and vec(b) are the position vectors of vec(A) and vec(B) respectively, then find the position vector of a point vec(C) and vec(BA) produced such that vec(BC) = 1.5 vec(BA) . Also, it is shown by graphically.

It the vectors vec(a), vec(b) and vec(c) form the sides vec(BC), vec(CA) and vec(AB) respectively of a triangle ABC, then write the value of vec(a) xx vec(c) + vec(b) xx vec(c) .

If vec(a), vec(b) and vec(c) are three vectors such that vec(a) + vec(b) + vec(c) = vec(0) , then prove that vec(a) xx vec(b) = vec(b) xx vec(c) = vec(c) xx vec(a) .