So the first step is to write those two as vectors.

And I'll call the vertical vector here A, and this vector, vector B.

So the vector A is simply 0I plus 3J.

The vector B is 3I plus 2J.

So now I can form the cross product, same way again, ijk.

And the vector A is 030.

The vector B is 320.

And when we compute this,

maybe you can see right away that these vectors lie in the xy plane, so

the only component that we are going to have here is the k component.

In other words in the z direction, which is perpendicular to this plane.

So, we know we are only going to get one component,

but nevertheless, we'll compute them all just to illustrate how that works.

So, the i component here, cross that out,

is 3 times 0- 2 times 0, which is indeed, 0.

The j component, is -0 times 0- 0 times 3,

which is also 0, as we know.

And finally, the k component,

the only one which is going to be non-zero

is equal to k times 0 times 3, 2- 3 times 3.

In other words, it's equal to minus 9k,

is the vector cross product.

But here we're only concerned with the magnitude, so

we don't care about the negative sign here, and the magnitude of

that vector is equal to the area, which is equal to 9, so the answer is c.

And this concludes our discussion of vectors.