# The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.

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The sum and difference of two vectors are perpendicular to each other. Prove that the vectors are equal in magnitude.

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As the vector $\vec A+\vec B$ and $\vec A-\vec B$ are perpendicular to each other, therefore

$(\vec A+\vec B).(\vec A-\vec B)=0$

$\vec A.\vec A-\vec A.\vec B+\vec B.\vec A-\vec B.\vec B=0$

or  A2 - B2 = 0

A = B  (∵ $\vec A.\vec B=\vec B.\vec A$)