The magnitudes of vectors A→ , B→ and C→

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The magnitudes of vectors A^{^→} , B^{^→} and C^{^→} are 3, 4 and 5 units respectively. If A^{^→} + B^{^→} = C^{^→} , then the angle between A^{^→} and B^{^→} is

1. π/2
2. cos^–1 0.6
3. tan^–1(7/5)
4. π/4

Correct Option: A

(A^{^→} + B^{^→})² = (C^{^→})²
⇒ A² + B² + 2 A^{^→}.B^{^→} = C²
⇒ 3² + 4² + 2 A^{^→}.B^{^→} = 5²
⇒ 2 A^{^→}.B^{^→} = 0
⇒ A^{^→}.B^{^→} = 0
∴ A^{^→} ⊥ B^{^→}
Here A² + B² = C².
Hence, A^{^→} ⊥ B^{^→}