I've gone about trying to solve this by assuming the x co-ordinate lies on the line, and then determining whether the other points lie on that line according to that ie.
If x = 5, then 5 = 2 + t, therefore t = 3. From this we can check that:
y = 3 - 3(3) = -6 and,
z = 4 + 2(3) = 10
From this we can tell that (5, -6, 10) does lie on the line
And if x = 3, then 3 = 2 + t, therefore t = 1. From this we can check that:
y = 3 - 3(1) = 0 and,
z = 4 + 2(1) = 6
From this we can tell that (3, 3,8) dies not lie on the line
Is this correct or am I doing something wrong?
Looks OK.
Alternatively, note from the parametric equations that $$t=x-2=1-\frac y3=\frac z2-2$$
For (5,-6, 10), $$x-2=1-\frac y3=\frac z2-2=3$$ Hence the point lies on the line.
For (3,3,8), $$x-2=1\neq1-\frac y3=0 \neq \frac z2-2=2$$ Hence the point does not lie on the line