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 $${{a}_{1}}{{\vec{r}}_{1}}+{{a}_{2}}{{\vec{r}}_{2}}+....+{{a}_{n}}{{\vec{r}}_{n}}=0$$ holds, then a similar equation will also hold w.r.t. to any other origin provided

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TuteeHUB · Accepted Answer

$${{a}_{1}}={{a}_{2}}={{a}_{3}}=....={{a}_{n}}=0$$

TuteeHUB · Answer

$${{a}_{1}}+{{a}_{2}}+....+{{a}_{n}}=n$$

TuteeHUB · Answer

$${{a}_{1}}+{{a}_{2}}+....+{{a}_{n}}=1$$

TuteeHUB · Answer

$${{a}_{1}}+{{a}_{2}}+....+{{a}_{n}}=0$$

1.	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 \[{{a}_{1}}{{\vec{r}}_{1}}+{{a}_{2}}{{\vec{r}}_{2}}+....+{{a}_{n}}{{\vec{r}}_{n}}=0\] holds, 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.	\[{{a}_{1}}={{a}_{2}}={{a}_{3}}=....={{a}_{n}}=0\]
Answer» D. \[{{a}_{1}}={{a}_{2}}={{a}_{3}}=....={{a}_{n}}=0\]

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