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Two vectors X and Y have equal magnitude. The magnitude of (X − Y) is n times the magnitude of (X + Y). The angle between X and Y is

1. cos⁻¹((n²−1)/(n²+1))
2. cos⁻¹((n²−1)/(−n²+1))
3. cos⁻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 vectors and the cosine of the angle between them. By applying the law of cosines to the expressions for the magnitudes of (X - Y) and (X + Y), we can establish a relationship that simplifies to the given expression for the angle.

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