Vectors: Solving a Trajectory on the x-y Plane

[discombobulated]

[SOLVED] vectors -

Homework Statement

At time t = 0 two forces f₁ = (i + j) and f₂ = (2i - 2j) start acting on a point body of unit mass lying stationary at the point (1,2) of the x,y plane. Describe the trajectory r(t) of the plane.

Homework Equations

F = ma

a = d²x/dt²

The Attempt at a Solution

Total force, F = (i + j) + (2i - 2j)
F = (3i - j)

I know I need to integrate using the acceleration equation but I'm confused by the x,y plane, I thought it was meant to be in i,j plane? :S Could someone please explain?
Thanks!

 

[Hootenanny]

i and j are unit vectors in the direction of the positive x and positive y direction respectively, so you're still working in the x-y plane.

 

[discombobulated]

thanks, so do i split it like this, d²x /dt² = 3 and d²y /dt² = -1 and then when I integrate to get x and y, put it back into i and j form?

 

[Hootenanny]

thanks, so do i split it like this, d²x /dt² = 3 and d²y /dt² = -1 and then when I integrate to get x and y, put it back into i and j form?

Sounds good to me