Expressing one Vector in terms of others

DistinctlyPlain

1. Homework Statement 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.

2. Homework Equations

R
3-1 = r1-Rs
R3-2 = r2-Rs

3. 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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Chan Pok Fung

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.

haruspex

Homework Helper
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2018 Award
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.

"Expressing one Vector in terms of others"

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