The vector sum of two forces is perpendicular | vedclass

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(C) Let the two forces be $\vec{A}$ and $\vec{B}$.The vector sum is $\vec{P} = \vec{A} + \vec{B}$.The vector difference is $\vec{Q} = \vec{A} - \vec{B

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are equal to each other in magnitude

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(C) Let the two forces be $\vec{A}$ and $\vec{B}$.The vector sum is $\vec{P} = \vec{A} + \vec{B}$.The vector difference is $\vec{Q} = \vec{A} - \vec{B}$.Since $\vec{P}$ and $\vec{Q}$ are perpendicular,their dot product must be zero:$\vec{P} \cdot \vec{Q} = 0$Substituting the expressions for $\vec{P}$ and $\vec{Q}$:$(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0$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 $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$,the middle terms cancel out:$|A|^2 - |B|^2 = 0$$|A|^2 = |B|^2$$|A| = |B|$Therefore,the forces are equal to each other in magnitude.

The vector sum of two forces is perpendicular to their vector difference. In that case,the forces

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