The vectors (vec{A} + vec{B}) and (vec{A} - v | vedclass

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(A) Two vectors are perpendicular if their dot product is zero.Given that $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ are perpendicular, their dot

Vedclass · Accepted Answer

$|\vec{A}| = |\vec{B}|$

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(A) Two vectors are perpendicular if their dot product is zero.Given that $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ are perpendicular, their dot product must be zero:$(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0$Expanding the dot product:$\vec{A} \cdot \vec{A} - \vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{A} - \vec{B} \cdot \vec{B} = 0$Since the dot product is commutative, $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$, so:$|\vec{A}|^2 - |\vec{B}|^2 = 0$$|\vec{A}|^2 = |\vec{B}|^2$$|\vec{A}| = |\vec{B}|$Thus, the condition is $|\vec{A}| = |\vec{B}|$.

The vectors $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ are perpendicular to each other. This is possible under the condition:

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