# Under what conditions does the equality | vector A + vector B | = | vector A − vector B | hold good?

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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.