I tried figuring out what's the geometrical meaning of this identity in vectors. Proving it isn't a problem, however I'd like to know a more geometry oriented explanation to it.I'd appreciate if someone could explain it to me. Thank you. ‖ a + b ‖ 2 + ‖ a − b ‖ 2 = 2 ( ‖ a ‖ 2 + ‖ b ‖ 2 )

Question

I tried figuring out what&#039;s the geometrical meaning of this identity in vectors. Proving it isn&#039;t a problem, however I&#039;d like to know a more geometry oriented explanation to it.I&#039;d appreciate if someone could explain it to me. Thank you.  ‖  a  +  b      ‖    2    +  ‖  a  −  b      ‖    2    =  2  (  ‖  a      ‖    2    +  ‖  b      ‖    2    )

Nirdaciw3 · Accepted Answer

I had the same question. I didn&#039;t know but the sum of the squares of the lengths of the four sides of a parallelogram seems to equal the sum of the squares of the lengths of the two diagonals. I don&#039;t remember I learned this property of parallelogram in middle school. I know the area is calculated as the base times altitude because the part sticking out can be tucked into the other side to make it rectangle. But this property is simple but significant enough that I should have learned it.