Question

A₁, A₂, A₃ ........A_n are the vertices of a regular plane polygon with n sides and 0 is its centre, then \(\sum \limits_{i = 1}^{n - 1} (\vec {OA}_i \times \vec {OA}_{i+1})=\) 

(a) \((n - 1) (\vec {OA_2} \times \vec {OA_1})\)

(b) \((1-n ) (\vec {OA_2} \times \vec {OA_1})\)

(c) \((n - 1) (\vec {OA_1} \times \vec {OA_2})\)

(d) \((1-n ) (\vec {OA_1} \times \vec {OA_2})\)

Answer 1

Correct options are (b) & (c).