Expressing one Vector in terms of others

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The discussion focuses on expressing the vector Rs in terms of the vectors r1 and r2, which represent positions relative to the center of mass between two bodies. The user attempts to relate r1 and r2 through the equation r2 = -(m1/m2)*r1 but feels uncertain about their approach. It is clarified that r1 and r2 are linearly dependent and span a one-dimensional space, indicating that Rs cannot be expressed as a linear combination of r1 and r2. The suggestion is made to redefine the vectors to facilitate expressing both positions in terms of Rs and r1. This highlights the importance of proper vector definitions in solving the problem.
DistinctlyPlain
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Homework Statement

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I am very rusty on my mathematics and I am wondering if there is a way to express Rs in terms of r1 and r2. The positions of the bodies are all relative to the origin 0 (C.o.M between m1 and m2). Basically I'm trying to express the two vectors coming from m3 in terms of the masses and position vectors for m1 and m2.

Homework Equations



R[/B]3-1 = r1-Rs
R3-2 = r2-Rs

The Attempt at a Solution



I think r1 and r2 are related through the expression: r2= -(m1/m2)*r1 but this was very much 'fudged' so I think I'm approaching the problem wrong.

Any help much appreciated.
Cheers.
 
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Clearly, r1, r2 are linearly dependent and span a 1-D space. Rs can never be an linearly combination of them. I think it would be more natural if you define that "r1-Rs" vector to be r1 and "r2-Rs" to be r2.
 
DistinctlyPlain said:
think r1 and r2 are related through the expression: r2= -(m1/m2)*r1
Yes, use that, so you can express both positions in terms of Rs and r1.
 
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