What are the diagonals of the cartesian products of the following sets?

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So, I'm doing Exercise 5. enter image description here

Here is what I think about a). enter image description here

So, we consider the first rectangle on the plane x y and the second on the plane x z. We take a point of the first rectangle and one of the second rectangle with the same coordinates. Proceeding like that, we obtain 'the diagonal of the parallelepiped.' So, I think it is more or less the correct answer. However, I cannot justify that.

If I am right, then b) is quite the same, but we have 'the diagonal plane of a three-dimensional coordinate system.'

I have no idea what to do with e). It seems impossible.