Two vectors vec{A} and vec{B} have equal magn | vedclass

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(A) Given that $|\vec{A}| = |\vec{B}|$. Let $\vec{R} = \vec{A} + \vec{B}$ and $\vec{D} = \vec{A} - \vec{B}$. Consider the dot product $\vec{R} \cdot \

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$\vec{A} - \vec{B}$

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(A) Given that $|\vec{A}| = |\vec{B}|$. Let $\vec{R} = \vec{A} + \vec{B}$ and $\vec{D} = \vec{A} - \vec{B}$. Consider the dot product $\vec{R} \cdot \vec{D} = (\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B})$. $= \vec{A} \cdot \vec{A} - \vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{A} - \vec{B} \cdot \vec{B}$. $= |\vec{A}|^2 - |\vec{B}|^2$. Since $|\vec{A}| = |\vec{B}|$,the dot product is $0$. Therefore,$\vec{A} + \vec{B}$ is perpendicular to $\vec{A} - \vec{B}$.

Two vectors $\vec{A}$ and $\vec{B}$ have equal magnitudes. Then the vector $\vec{A} + \vec{B}$ is perpendicular to:

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