Find vectors that satisfy the following conditions
Find vectors and \in \mathbb{R}^3 that simultaneously satisfy all of the following:

 is parallel to (2,1,5)
 is perpendicular to (2,1,5)
I understand what each condition means in terms of how it affects the vectors I am trying to find; however, I can't seem to relate them enough to derive the actual vectors. I know that:
and
also that
How do I go about finding the two vectors that satisfy these conditions other than trial and error?
Thanks.
Re: Find vectors that satisfy the following conditions
from u1 = 2m, u2 = m, u3 = 5m, and u1v1 = 3, u2v2 = 4, u3v3 = 10 we have:
v1 = u1  3 = 2m  3
v2 = u2  4 = m  4
v3 = u3  10 = 5m  10.
from 2v1 + v2 + 5v3 = 0, we have:
2(2m3) + m4 + 5(5m10) = 0, so
4m  6 + m  4 + 25m  50 = 0
30m = 60
m = 2.
hence u = (4,2,10) and v = (1,2,0).