Finding the volume in a cylinder that is intersected by a plane

I have a homework question that goes as follows.

Let $V=\{(x,y,z):{x}^{2}+{y}^{2}\le 4\text{and}0\le z\le 4\}$ be a cylinder and let P be the plane through (4, 0, 2), (0, 4, 2), and (-4, -4, 4). Compute the volume of C below the plane P.

So I have these points and I set up my $a(x-{x}_{0})+b(y-{y}_{0})+c(z-{z}_{0})=0$ where $({x}_{0},{y}_{0},{z}_{0})$ is a point in the plane and ⟨a, b, c⟩ is perpendicular.

I then got two vectors that go between two points, namely:

$PQ=<(0-4,(4-0),(2,-2)>=<-4,4,0>$ and $PR=<(-4-4),(-4-0),(4,-2)>=<-8,-4,2>$

I then get the cross product of them to get $<8,8,48>$ which is the coefficient in my equation of the plane:

$8(x-4)+8(y-0)+48(z-2)=0$

I think that this is the equation of my plane. Is it?

I have a homework question that goes as follows.

Let $V=\{(x,y,z):{x}^{2}+{y}^{2}\le 4\text{and}0\le z\le 4\}$ be a cylinder and let P be the plane through (4, 0, 2), (0, 4, 2), and (-4, -4, 4). Compute the volume of C below the plane P.

So I have these points and I set up my $a(x-{x}_{0})+b(y-{y}_{0})+c(z-{z}_{0})=0$ where $({x}_{0},{y}_{0},{z}_{0})$ is a point in the plane and ⟨a, b, c⟩ is perpendicular.

I then got two vectors that go between two points, namely:

$PQ=<(0-4,(4-0),(2,-2)>=<-4,4,0>$ and $PR=<(-4-4),(-4-0),(4,-2)>=<-8,-4,2>$

I then get the cross product of them to get $<8,8,48>$ which is the coefficient in my equation of the plane:

$8(x-4)+8(y-0)+48(z-2)=0$

I think that this is the equation of my plane. Is it?