Proving this line lies on this plane with a specfic equaction

Q.Does the line with equation (x, y, z) = (5, -4, 6) + u(1,4,-1) lie in the plane with equation (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)? Justify your answer algebraically.

What I tried doing:

I started by getting the parametric equation of (x, y, z) = (5, -4, 6) + u(1,4,-1)

x=5+u

y=-4+4u

z=6-u

I then subbed in u=0 to get a set of points

x=5

y=-4

z=6

I then got the parametric equation for (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)

x=3+s+2t

y=0+s-t

z=2-s+t

I decided to use the points (5,-4,6) and sub them into

x=3+s+2t

y=0+s-t

z=2-s+t

5=3+s+2t

5-3=s+2t

2=s+2t

-4=0+s-t

-4+0=s-t

-4=s-t

6=2-s+t

6-2=-s+t

4=-s+t

I don't know if I'm doing this correctly. I really don't know what to so I tried that.(Thinking)