Write the planes equation when given parametric form. This should be an easy question:
Lets say we have a plane $(P)$ equation on parametric form:
$(P) : x,y,z = (0,2,0) + t(0, \frac{-4}{3}, \frac{1}{3}) + s(\frac{1}{3}, \frac{-4}{3}, 0)$ 
We want to write this plane on the form $Ax + By + Cz + D = 0$.
My way of doing this calculation is to write out the determinant of the matrix with the equations from the parametric form, like this:
$$A = \left( \begin{matrix} x-0 & 0 & \frac{1}{3} \\ y-2 & \frac{-4}{3} & \frac{-4}{3} \\ z-0& \frac{1}{3} & 0 \end{matrix}\right )$$
After some calculations this gives me the following result: $\frac{4}{9}x - \frac{1}{9}y+ \frac{4}{9}z - \frac{2}{9} = 0$
Now my math book  says that the correct answer is : $4x - 1y+ 4z - 2= 0$
What have I done wrong? (Or is there an error in my text book, it has happen before...)
Thank you!

As DonAntonio said in the comment above, multiply the equation by 9 and you have the answer!
