How can I find the affine subspace $\pi$ that contains the following points?

$ P:(1,0,2,0,1)\\
Q:(0,1,0,1,0)\\
R:(2,0,1,0,2)$

Surely it is easy in $\mathbb R^3$, but I don't understand how can I determinate $\pi$ and the distance between the points in $\mathbb R^5$! (I need these information because I have to determine the area of the triangles that has P Q and R as vertices)