Let be the position vectors of points relative to an origin

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let r1,r2,r3,…,rnr_1, r_2, r_3, \dots, r_n be the position vectors of points P1,P2,P3,…,PnP_1, P_2, P_3, \dots, P_n relative to an origin OO . Show that if the vectors equation a1r1+a2r2+⋯+anrn=0a_1 r_1 + a_2 r_2 + \dots + a_n r_n = 0 holds, then a similar equation will also hold good with respect to any other origin O′O' , if a1+a2+a3+⋯+an=0a_1 + a_2 + a_3 + \dots + a_n = 0 .

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