The vectors A→ and B→ are such that |A→ +

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The vectors A^{^→} and B^{^→} are such that |A^{^→} + B^{^→}| = |A^{^→} - B^{^→}| The angle between the two vectors is

1. 60°
2. 75°
3. 45°
4. 90°

Correct Option: D

|A^{^→} + B^{^→}|² = |A^{^→} - B^{^→}|²
= | A^{^→} |² + | B^{^→} |² + 2A^{^→} . B^{^→} = A² + B² + 2AB cosθ
= |A^{^→} - B^{^→}|² = | A^{^→} |² + | B^{^→} |² - 2A^{^→} . B^{^→}
= A² + B² - 2AB cosθ
So , A² + B² + 2AB cosθ = A² + B² - 2AB cosθ
4AB cosθ = 0 ⇒ cosθ = 0
⇒ θ = 90°
So, angle between A & B is 90°.