Find an equation of the plane that passes through the points

Find an equation of the plane that passes through the points P, Q, and R. P(3, 1/3, -9), Q(2, 2/3, -3), R(5, 0, 1) ______________

We have two vectors from these points:

PQ = OQ - OP = ( -1 , 1/3 , 6)

PR = OR - OP = ( 2 , -2/3 , 4 )

Cross Product : PQ x PR = (16/3 , 16 , 0)

equation of plane : ax +by +cz = d where (a, b, bc) is the normal vector

a = 16/3 , b = 16 , c=0

So, 16x/3 + 16y = d.Plug ( 3, 1/3 , -9) to get d

(16/3)*3 + 16(1/3) = d

d = 16 +16/3 = 64/3

So, 16x/3 + 16y - 64/3

16x + 48y - 64 =0 (Equation of Plane)