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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  (∵ \(\vec A.\vec B=\vec B.\vec A\))

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