If Q is the point of intersection of the medians of a triangle ABC, prove that `vec(QA)+vec(QB)+vec(QC)=vec0`.

G is the centroid of a triangle ABC, show that : vec(GA)+vec(GB)+vec(GC)=vec0 .

If O and H be the circumcentre and orthocentre respectively of triangle ABC, prove that vec OA+ vec OB+ vec OC= vec OH .

If S and O be the circumcentre and orthocentre respectively of triangle ABC, prove that vec SA + vec SB + vec SC= vec SO .

ABCD is a parallelogram and P the intersection of the diagonals, O is any point . Show that vec(OA)+vec(OB)+vec(OC)+vec(OD)=4vec(OP) .

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

If a,b,c are the lengths of the sides [BC],[CA] and [AB] of triangle ABC, prove that vec BC+ vec CA + vec AB= vec 0 and deduce that frac {a}{sin A}=frac {b}{sin B}=frac {c}{sin C} .

If vec a ,\ vec b ,\ vec c be the vectors represented by theside sof a triangle, taken in order, then prove that vec a+ vec b+ vec c= vec0dot

If ABC is triangle and D is the mid-point of [BC], prove that vec AB + vec AC= 2 vec AD .

Given an equilateral triangle ABC with side length equal to 'a'. Let M and N be two points respectivelyАВIn the side AB and AC such that vec(AN) = Kvec(AC) and vec(AM) = vec(AB)/3 If vec(BN) and vec(CM) are orthogonalthen the value of K is equal to

If veca , vec b , vec c are the position vectors of the vertices A ,B ,C of a triangle A B C , show that the area triangle A B Ci s1/2| vec axx vec b+ vec bxx vec c+ vec cxx vec a|dot Deduce the condition for points veca , vec b , vec c to be collinear.