Class 12

Math

Algebra

Vector Algebra

Let $r_{1},r_{2},r_{3},,r_{n}$ be the position vectors of points $P_{1},P_{2},P_{3},P_{n}$ relative to the origin $O˙$ If the vector equation $a_{1}r_{1}+a_{2}r_{2}++a_{n}r_{n}=0$ 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. $a_{1}=a_{2}=a_{3}+˙ a_{n}=0$