Finding F2 when F1 and net acceleration are known

[NeverSummer]

Homework Statement

Two forces F1 and F2 are acting on a mass M=4kg. The force F1 = 7i + 6j + 8k, in N. The acceleration of the mass is given by a = 1i + 3j + 2k, in m/s2. Calculate the magnitude of F2 .

Homework Equations

F=ma

The Attempt at a Solution

F1+F2=ma
m=4kg
F1=sqrt(7^2+6^2+8^2) = 12.2066N
a=sqrt(1^2+3^2+2^2) = 3.71466m/s

plug it all in and I get F2=2.7601N


I have no idea what I'm doing wrong, so if some one would point me in the right direction, that would be great.

 

[cupid.callin]

find the F2 force in vector form and then find its mag!

 

[verty]

I can't follow what you are doing. My thought was calculate the components of F2, then calculate the magnitude.

 

[NeverSummer]

Thanks! That was my problem, my brain was burnt out so I just tried to do it all in one go rather than by components. Didn't work :P

 

[cupid.callin]

I can't follow what you are doing. My thought was calculate the components of F2, then calculate the magnitude.

I said the same thing!

Mag of force will will give wrong answer as the 2 forces might not be parallel!
the way you did is only useful when forces act parallel but in this case you don't know if they are or not.

find the component of F2 and then force !