Finding the Total Momentum of a Three Particle System

[Westin]

Homework Statement

Consider a system consisting of three particles:

m1=5kg, v1=

-6,6,7

m

s

m2=7kg, v2=

8,-6,-7

m

s

m3=1kg, v3=

6,7,13

m

s

What is the total momentum of this system?

What is the velocity of the center of mass of this system?[/B]

Homework Equations

p=m*v

The Attempt at a Solution

I tried (m1+m2)(v1+v2) + (m2+m3)(v2+v3)
and (m1+m2+m3)(v1+v2+v3), neither were correct...

 

[AlephNumbers]

To find the momentum of the system of particles, add the momentums of each of the particles. The momentum of each particle is the mass of each particle multiplied by each particle's respective velocity.

I tried (m1+m2)(v1+v2) + (m2+m3)(v2+v3)

Foiling the first two factors produces m₁v₁ + m₂v₂ + m₁v₂ + m₂v₁. Why would you multiply the mass of one of the particles by the velocity of another particle? How could this result be meaningful?