Assignment:
The Pythagorean Theorem can also be proved directly, by choosing 0 at the right angle of a right-angled triangle whose other two vertices are u and v.
Show that |v - u|^2 = |u|^2 + |v|^2 under these conditions, and explain why this is the Pythagorean theorem.
Provide complete and step by step solution for the question and show calculations and use formulas.