The vector sum of two forces is perpendicular | vedclass

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(C) Let the two forces in vector form be $\vec{A}$ and $\vec{B}$.Their vector sum is $(\vec{A} + \vec{B})$ and their vector difference is $(\vec{A} -

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are equal to each other in magnitude

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(C) Let the two forces in vector form be $\vec{A}$ and $\vec{B}$.Their vector sum is $(\vec{A} + \vec{B})$ and their vector difference is $(\vec{A} - \vec{B})$.Since the vector sum and vector difference are perpendicular to each other,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 the terms cancel out:$|\vec{A}|^2 - |\vec{B}|^2 = 0$$|\vec{A}|^2 = |\vec{B}|^2$$|\vec{A}| = |\vec{B}|$Therefore,the two forces are equal in magnitude.

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

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