The vector sum of the two forces vec{A} and v | vedclass

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(D) Given that the vector sum $(\vec{A} + \vec{B})$ is perpendicular to the vector difference $(\vec{A} - \vec{B})$.Two vectors are perpendicular if t

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equal in magnitude

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(D) Given that the vector sum $(\vec{A} + \vec{B})$ is perpendicular to the vector difference $(\vec{A} - \vec{B})$.Two vectors are perpendicular if their dot product is zero.Therefore, $(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0$.Expanding the dot product, we get $\vec{A} \cdot \vec{A} - \vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{A} - \vec{B} \cdot \vec{B} = 0$.Since the dot product is commutative, $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$.Thus, $|\vec{A}|^2 - |\vec{B}|^2 = 0$.This implies $|\vec{A}|^2 = |\vec{B}|^2$, which means $|\vec{A}| = |\vec{B}|$.Hence, the forces $\vec{A}$ and $\vec{B}$ are equal in magnitude.

The vector sum of the two forces $\vec{A}$ and $\vec{B}$ is perpendicular to their vector difference. Hence, the forces $\vec{A}$ and $\vec{B}$ are

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