Trouble dealing with vector coordinates in question

[bushabean]

Homework Statement

A rocket is to rendezvous with a satellite and needs to make a course adjustment.
the rocket has a velocity = (10 + 0 + 0) ms−1 relative to the satellite and mission control has sent a command to the rocket side thruster to exert a thrust = (0 − 100 + 0) N for 100 seconds.

(i) What is the force exerted on the rocket from the side thruster in vector coordinates?

(ii) Calculate the momentum of the rocket in vector coordinates after the thruster has operated. (3)

2. Homework Equations
Ft = mv - mu
p = mv
F = ma
a = Δv/Δt

The Attempt at a Solution

(i) I assume this is the equal and opposite force? being (0 +100 + 0)

(ii) I feel there are many ways to tackle this problem but every time I fail. Is the force (0 +100 + 0) after the 100s or do I have to multiply it by the time, assuming that (0 +100 + 0) is even correct? I tried doing:

F = ma
100 = 1000 * a
a = 1/10 m/s^2

a = Δv/Δt
0.1 = Δv/100
Δv = 10m/s

add that 10m/s to the to get (10 + 10 + 0)

Take the magnitude of the velocity to get 10√2

p = mv
p = 1000 * 10√2
p = 14142.1 kgm/s

But that seems so complicated it just can't be true. Any help would be appreciated :)

 

[haruspex]

(i) I assume this is the equal and opposite force? being (0 +100 + 0)

I don't see why. If the command is to exert thrust 0,-100,0 then that is the thrust it should exert.

 

[haruspex]

p = 14142.1 kgm/s

Read the question:

momentum of the rocket in vector coordinates