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Let r(1),r(2),r(3), . . .,r(n) be the po...

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 an origin O. show that if then a similar equation will also hold good with respect to any other origin O'. If `a_(1)+a_(2)+a_(3)+ . . .+a_(n)=0`.

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To solve the problem, we need to show that if \( a_1 + a_2 + a_3 + \ldots + a_n = 0 \), then a similar equation will hold true with respect to any other origin \( O' \). ### Step-by-Step Solution: 1. **Define Position Vectors**: Let \( \mathbf{r}_1, \mathbf{r}_2, \ldots, \mathbf{r}_n \) be the position vectors of points \( P_1, P_2, \ldots, P_n \) relative to the origin \( O \). 2. **Introduce New Origin**: ...
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