Expressing one Vector in terms of others

[DistinctlyPlain]

Homework Statement

I am very rusty on my mathematics and I am wondering if there is a way to express R_s 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-R_s
R_3-2 = r₂-R_s

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.

 

[Mayan 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]

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.