If the magnitude of sum of two vectors is equal to the magnitude

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If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is :

1. 0°
2. 90°
3. 45°
4. 180°

Correct Option: B

|A^{^→} + B^{^→}| = |A^{^→} - B^{^→}|
Squaring on both sides
|A^{^→} + B^{^→}|² = |A^{^→} - B^{^→}|²
⇒ A^{^→} . A^{^→} + 2A^{^→} . B^{^→} + B^{^→} . B^{^→} = A^{^→} . A^{^→} - 2A^{^→} . B^{^→} + B^{^→} . B^{^→}
⇒ 4A^{^→} . B^{^→} = 0 ⇒ 4A^{^→} . B^{^→} cos θ = 0
⇒ cos θ = 0 ⇒ θ = 90°