`A_1,A_2,..., A_n` are the vertices of a regular plane polygon with n sides and O as its centre. Show that `sum_(i=1)^n vec (OA)_i xx vec(OA)_(i+1)=(1-n)(vec (OA)_2 xx vec(OA)_1)`

A_(1),A_(2),...,A_(n) are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^(n)vec OA_(i)xxvec OA_(i+1)=(1-n)(vec OA_(2)xxvec OA_(1))

Suppose A_(1), A_(2), …, A_(5) are vertices of a regular pentagon with O as centre. If sum_(i=1)^(4)(OA_(i) times OA_(i+1))=lambda(OA_(1) times OA_(2)) then lambda= _______

Let O be the centre of the regular hexagon ABCDEF then find vec(OA)+vec(OB)+vec(OD)+vec(OC)+vec(OE)+vec(OF)

ABCD is a quadrilateral and E is the point of intersection of the lines joining the middle points of opposite side. Show that the resultant of vec (OA) , vec(OB) , vec(OC) and vec(OD) = 4 vec(OE) , where O is any point.

Given a regular hexagon ABCDEF with centre o,show that vec OB-vec OA=vec OC-vec OD

If A_1A_2....A_n is a regular polygon. Then the vector vec(A_1A_2)+vec(A_2A_3)+.....vec(A_nA_1) is

Let O be the centre of a regular pentagon ABCDE and vec(OA) = veca , then vec(AB) +vec(2BC) + vec(3CD) + vec(4DE) + vec(5EA) is equals:

Let O be the centre of a regular pentagon ABCDE and vec(OA) = veca , then vec(AB) +vec(2BC) + vec(3CD) + vec(4DE) + vec(5EA) is equals:

Let O, O' and G be the circumcentre, orthocentre and centroid of a Delta ABC and S be any point in the plane of the triangle. Statement -1: vec(O'A) + vec(O'B) + vec(O'C)=2vec(O'O) Statement -2: vec(SA) + vec(SB) + vec(SC) = 3 vec(SG)