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Two vectors P and Q have equal magnitudes. If the magnitude of P + Q is n times the magnitude of P − Q, then angle between P and Q is -

1. sin⁻¹((n−1)/(n+1))
2. cos⁻¹((n−1)/(n+1))
3. sin⁻¹((n²−1)/(n²+1))
4. cos⁻¹((n²−1)/(n²+1))

Correct answer: cos⁻¹((n²−1)/(n²+1))

Solution

The correct option is derived from the relationship between the magnitudes of the sum and difference of two vectors, which can be expressed in terms of the cosine of the angle between them. By applying the law of cosines and manipulating the resulting equations, we find that the angle can be expressed as cos⁻¹((n²−1)/(n²+1)), which matches the given condition.

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