Determine whether the given planes are parallel:

$\displaystyle 4x-y+2z=5$

$\displaystyle 7x-3y+4z=8$

I think I can find a vector that is parallel to each plane, but I am not quite sure how to compare the vectors that I find. Here is what I have done:

I tried to find 2 points on each that satisfied the equations then found the vector joining the two points...

$\displaystyle 4(1)-(-1)+2(0) = 5 \rightarrow (1,-1,0)$

$\displaystyle 4(0)-(-1)+2(2) = 5 \rightarrow (0,-1,2)$

$\displaystyle \vec{v} = <1,0,-2>$

$\displaystyle 7(0)-3(0)+4(2) = 8 \rightarrow (0,0,2)$

$\displaystyle 7(1)-3(1)+4(1) = 8 \rightarrow (1,1,1)$

$\displaystyle \vec{r} = <-1,-1,1>$

How do I check to see if $\displaystyle \vec{v}$ and $\displaystyle \vec{r}$ are parallel?

Can I solve this using an augmented matrix maybe?