Vector-based Christmas Decoration Balancing at Origin | Homework Solution

[smileandbehappy]

Homework Statement

A christmas decoration consitse of a 15 gram ball at (1,1,1), a 5 gram ball at (2,-1,0) and a 10 gram ball joined with thin wires. Where should the decoration be placed if the decoration is to balance at the origin?

Homework Equations

The Attempt at a Solution

Err... well not that much. I have worked out that the 3rd ball is going to have to blance with the other two but that's about it. Can you please NOT do this for me but rather nudge me towarsds what i should be doing.
Many thanks

 

[Sourabh N]

For balancing, centre of mass should lie at origin. Do you know how to calculate the position of centre of mass of 3-body system?

 

[smileandbehappy]

No i dont.

 

[Sourabh N]

For an n-body system, COM = (M1*r1 + M2*r2 + ... + Mn*rn)/(M1 + M2 + ... + Mn).

 

[Sourabh N]

for (1,1,1) : r = \hat{i} +\hat{j} +\hat{k}

 

[smileandbehappy]

i get the answer to be (2.5, -1,-1.5) is this correct?

 

[Sourabh N]

Nope. It should be (-2.5,-1,-1.5).