Let ` vec r_1, vec r_2, vec r_3, .....vec r_n` be the position vectors of points `P_1,P_2, P_3 ,......P_n` relative to the origin `O`. If the vector equation `a_1 vec r_1+a_2 vec r_2+.....a_n vec r_n=0` hold, then a similar equation will also hold w.r.t. to any other origin provided a) `a_1+a_2+......a_n=n` b) `a_1+a_2+....a_n=1` c) `a_1+a_2+....a_n=0` d) `a_1=a_2=a_3+a_n=0`