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 :

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Given X = Y X 2 + Y 2 - 2 × Y cos θ = n X 2 + Y 2 + 2 × Y cos θ Square both sides 2 X 2 ( 1 - cos θ ) = n 2 · 2 X 2 ( 1 + cos θ ) 1 - cos θ = n 2 + n 2 cos θ cos θ = 1 - n 2 1 + n 2 θ = cos - 1 n 2 - 1 - n 2 - 1

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