Three forces act on a particle that moves with a constant ve

Three forces act on a particle that moves with a constant velocity v = 2 m/sx - 7m/sy. Two forces acting on this particle are F_1 = -2 Nx - 10 Ny - 6Nz and F_2 = -3 Nx + 4Ny - 6Nz. What are the vector components and the magnitude of the third force? Components Magnitude

Solution

since velocity is constant, net force should be 0

so,
F1 + F2 + F3 = 0
(-2x -10 y - 6z) + (-3 x + 4y - 6z) + F3 = 0
(-5x - 6y -12 z) + F3 = 0
F3 = ( 5x + 6y +12 z) N

components:
x = 5
y = 6
z = 12

magnitude = sqrt (5^2 + 6^2 + 12^2) = 14 N