Hi,can someone please explain how to solve this question to me. 1) For any two vectors u and v, prove that |u + v|^2 + |u -v|^2 = 2(|u|^2 + |v|^2) In proving this, what geometric fact have your proved? Thanks heaps!!
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Originally Posted by Vishak Hi,can someone please explain how to solve this question to me. 1) For any two vectors u and v, prove that |u + v|^2 + |u -v|^2 = 2(|u|^2 + |v|^2) In proving this, what geometric fact have your proved? Thanks heaps!! Hi Vishak! Note that . Can you simplify that?
I'm not sure what the triangle brackets mean, but ill guess - is it just u^2 + 2uv + v^2?
Originally Posted by Vishak 1) For any two vectors u and v, prove that |u + v|^2 + |u -v|^2 = 2(|u|^2 + |v|^2) In proving this, what geometric fact have your proved? Surely you must know that Moreover, if vectors are adjacent sides of a parallelogram then are its diagonals.
Thanks guys, what about the second part - "what geometric fact have you proved?"
Originally Posted by Vishak I'm not sure what the triangle brackets mean, but ill guess - is it just u^2 + 2uv + v^2? The triangle brackets are one of the ways you can write a dot product of vectors. You can also write it as . And yes, that is what it is. Originally Posted by Vishak Thanks guys, what about the second part - "what geometric fact have you proved?" Care to guess now that you know that are adjacent sides of a parallelogram and are its diagonals?
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