Determine points on lines meeting planes :S

Determine the equations of the line joining A(5, 1, 3) and B(2, 3, 6), both in parametric and cartesian forms.
This line meets the plane with equation

x + 3y - 2z = 6

in the point C. Determine the coordinates of C.

Thank you in advance guys.

B - A
= (2, 3, 6) - (5, 1, 3)
= (-3, 2, 3)

Parametric:
x = 5 - 3t, where t is an arbitrary scalar.
y = 1 + 2t
z = 3 + 3t

Cartesian:
(x , y, z) = (5, 1, 3) + t(-3, 2, 3)

Now for the intersection:
x + 3y - 2z = 6
(5 - 3t) + 3(1 + 2t) - 2(3 + 3t) = 6
5 - 3t + 3 + 6t - 6 - 6t = 6
-3t + 2 = 6
-3t = 4
t = -4/3

For the point C, we have:
x = 5 - 3t = 5 - 3(-4/3) = 9
y = 1 + 2t = 1 + 2(-4/3) = -5/3
z = 3 + 3t = 3 + 3(-4/3) = -1

C = (9 , -5/3, -1)