If the vectors a=(2,3,4) and b=(10,y,z) are perpendicular, how must y and z be related?

so this is what I did:

(2,3,4) . (10,y,z)=0

20+3y+4z=0

y=-20/3 - 4z/3

z=-5 - 3y/4

is this ok? there are no answers in the back of the book, so I am not sure. thanks for your help!