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Homework Statement
Show that (u+v)dot(u-v)=0 iff |u| = |v|
Homework Equations
if u= x1, y1
and if v= x2, y2
then u dot v= x1x2 + y1y2
The Attempt at a Solution
((x1+x2),(y1+y2)) dot ((x1-x2),(y1-y2))=
(x1^2-x2^2)+(y1^2-y2^2)=
if |u|=|v| then sqr(x1^2+y1^2)=sqr(x2^2+y2^2)
x1^2+y1^2=x2^2+y2^2
Now back to problem
x1^2+y1^2-x2^2-y2^2=0
let x1^2+y1^2=a
since x1^2+y1^2=x2^2+y2^2, x2^2+y2^2=a
a-a=0
i've shown the if part but how do I show the iff part?