Question

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

Answer 1

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