Math Help - Vector Problem

Hi,
Find vectors v & w be such that v is orthogonal to u = (2, -1, 4), v + w = (-2, 3, 1) & w is parallel to u
Thankyou in advance for any assistance provided.

I think v=(-32/19,54/19,31/19) w=(-6/19,3/19,-12/19) is be the solution.

you have to solve 4 equations simultaniously:
w=a*(2,-1,4) for some a
w=(2a,-a,4a)
also let v=(x,y,z)
v dot u=0 => 2x-y+4z=0
if you now use that v+w=(-2,3,1) you have 4 equations and 4 unknowns.