The vector sum of two forces is perpendicular to their vector

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

1. cannot be predicted
2. are equal to each other
3. are equal to each other in magnitude
4. are not equal to each other in magnitude

Correct Option: C

P^{^→} = vector sum = A^{^→} + B^{^→}
Q^{^→} = vector differences = A^{^→} - B^{^→}
Since P^{^→} and Q^{^→} are perpendicular
∴ P^{^→} . Q^{^→} = 0 ⇒ (A^{^→} + B^{^→}) . (A^{^→} - B^{^→}) = 0
⇒ A² = B² ⇒ | A^{^→} | = | B^{^→} |