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Under what conditions does the equality | \(\vec A+\vec B\) | = | \(\vec A-\vec B\) | hold good?

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\(|\vec A+\vec B|=|\vec A-\vec B|\)

\((\vec A+\vec B)^2=(\vec A-\vec B)^2\)

or  = \(A^2+B^2+2\vec A.\vec B\)

=\(A^2+B^2-2\vec A. \vec B\)

or \(4\vec A.\vec B=0\)

This implies that \(\vec A\) and \(\vec B\) are perpendicular to each other.

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