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Question:

Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to n times the magnitude of A - B, then the angle between A and B is

cos⁻¹(n/(n+1))

cos⁻¹(n²/(n²+1))

sin⁻¹(n/(n+1))

sin⁻¹(n²/(n²+1))

Solution:

|A+B|=n|A−B|⇒(A²+B²+2ABcosθ)=n²(A²+B²−2ABcosθ)
It is given that |A|=|B|
Hence cosθ=(n²−1)/(n²+1) ⇒θ=cos⁻¹((n²−1)/(n²+1))