Two vectors and have equal magnitudes

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Two vectors A⃗\vec{A} and B⃗\vec{B} have equal magnitudes. The magnitude of (A⃗+B⃗)(\vec{A} + \vec{B}) is 'n' times the magnitude of (A⃗−B⃗)(\vec{A} - \vec{B}) . The angle between A⃗\vec{A} and B⃗\vec{B} is: (1) cos⁡−1[n2−1n2+1]\cos^{-1}\left[\frac{n^2 - 1}{n^2 + 1}\right] (2) cos⁡−1[n−1n+1]\cos^{-1}\left[\frac{n - 1}{n + 1}\right] (3) sin⁡−1[n2−1n2+1]\sin^{-1}\left[\frac{n^2 - 1}{n^2 + 1}\right] (4) sin⁡−1[n−1n+1]\sin^{-1}\left[\frac{n - 1}{n + 1}\right]

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