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If a and b are two unit vectors and θ is the angle between them, then a+b is a unit vector if θ is

  • dps -

    without loss of generality, we can let

    a = <1,0>
    b = <cosθ,sinθ>

    a+b = <(1+cosθ),sinθ>
    |a+b|^2 = (1+cosθ)^2 + sin^2 θ
    if a+b is a unit vector,
    |a+b|^2 = 1

    1+2cosθ+cos^2θ + sin^2θ = 1
    1+2cosθ = 0
    cosθ = -1/2
    θ = 2pi/3

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