`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-1) 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 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 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 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 ars its centre. Show that sum_(i=1)^(n-1) (vec(OA_(i))xxvec(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 ars its centre. Show that sum_(i=1)^(n-1) (vec(OA_(i))xxvec(OA)_(i+1))=(n-1) (vec(OA)_1 xx vec(OA)_(2))

If A_(1), A_(2), ……A_(n) are the vertices of a regular polygon with 'n' sides and O is its centre then sum_(i=1)^(n-1) bar(OA_(i)) xx bar(OA)_(i+1)=…

A_(1), A_(2), A_(3), ……,A_(n) are the vertices of a regular plane polygon of n slides and O is the centre then show that underset(i=1)overset(n-1)Sigma bar(OA_(i)) xx bar(OA)_(i+1) = (1-n) (bar(OA)_(2) xx bar(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 A_1,A_2,....A_n be the vertices of an n-sided regular polygon such that , 1/(A_1A_2)=1/(A_1A_3)+1/(A_1A_4) . Find the value of n.