Determining p and q in Equilibrium

[Lavace]

Homework Statement

Three forces F1, F2 and F3 act on a particle.
F1 = (-3i + 2pj)N F2 = (pi + 3qj)N F3 = (qi - 7j)N

Given that the particle is in equilbirum, determine the value of p and the value of q.

Homework Equations

(-3i + 2pj) + (pi + 3qj) + (qi - 7j) = 0

The Attempt at a Solution

Well, its in equilbirum, so I figured all the forces added together would equal 0. Now, because there's more then one unknown, one thing to do is to use is Simultanious Equations, but I'm finding it difficult cause I'm unsure of how to make the simultanious equations, which is meant to be basic at my level =/.

Any hints/help is very appreciated =) However, it is a Sunday after all ;)

 

[Doc Al]

Since force is a vector, each component must be separately equal to zero. So write two equations: one for the i component, one for the j component. Those are the two equations that you'll have to solve simultaneously.

 

[Lavace]

Still slightly confused, so essentially is this something along the right lines:
pi = 3i -2pj -3qi -qi +7j

And then the same for qi? But then I'd be wrong, cause it'd be the same statement but with -pi instead of -qi.

 

[Doc Al]

No. First add up all the i components, set that equal to zero. That's one equation. Then do the same for the j components. That's the second equation.

 

[Lavace]

Ahhh! Thank you for all your help!
-3 + p + q = 0 (All the i values)
2p + 3q - 7 = 0 (All the j values)

-3 + p + q = 2p + 3q - 7
4 -2q = p (We now have a statement for p, to sub in)

3 - p = q
3 - 4 + 2q = q
q = -3 + 4
q = 1

Sub 1 into:
3 - q = p
p = 2.

And those are the correct answers!
Thank you for all your help! =)