Question

θ is the angle between two vectors a and b,show that 1/2 |a+b|=Cos θ/2

Answer 1

Answer:

This diagram gives a geometric interpretation. The angle between the unit vectors A and B is theta, and they form two congruent triangles with the green line that is the perpendicular bisector of A+B. Clearly, θ=λ+λ , so cos(θ/2)=cos(λ)=12|A+B|/|A|=12|A+B|