Using vectors, the dot product, and the cross product, prove that the sum of the squares of the diagonals of a parallelogram is equal to twice the sum of the squares of two adjacent sides of the parallelogram.
The Attempt at a Solution
I used the Pythagorean theorem to solve it easily. But I don't know how to solve it using vectors. Is the problem expecting me to draw a parallelogram using arrows? I could create the same triangle I made to solve it using the P-theorem, but that would just be making a triangle. I need to make a parallelogram. It seems like the best the dot and cross product could do is tell me the angle of the triangle. I don't see how it's going to give me the square of anything.