Prove <mrow class="MJX-TeXAtom-ORD"> | </mrow> x + y <mrow class="MJX-

anginih86

anginih86

Answered question

2022-06-15

Prove | x + y | 2 + | x y | 2 = 2 | x | 2 + 2 | y | 2 if x , y R k .
Interpret this geometrically, as a statement about parallelograms.
I've shown that the expression given equates to x x + 2 x y + y y + x x 2 x y + y y. But what does this have to do with parallelograms?

Answer & Explanation

lorienoldf7

lorienoldf7

Beginner2022-06-16Added 19 answers

Remember that x and y are vectors. Then if you form a parallelogram with sides x and y , then x y is the short diagonal and x + y is the long diagonal (assuming you labelled the sides sensibly)
fabios3

fabios3

Beginner2022-06-17Added 10 answers

The points, 0, x, y, x + y form a parallelogram.

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