What Are the Possible Values of v2 Dot v3 and Angles Between Them in R^n?

[Punkyc7]

Three unit vectors v1 v2 and v3 are in R^n. We are told that v1 dot v2= v1 dot v3=1/2. What are the possible values of v2 dot v3. What could the angle be between the vectors v2 and v3 give example for the cases in R^2 and R^3.

costheta = (x dot y)/((magnitude of x)(magnitude of y)


I tried using the cauchy schwarts inequality and i got the angle to be between pi/3 and 5pi/3 in R^2. I am not sure how to do R^3 or how to find the values for v2 dot v3? I am assuming that v2 dot v3 must be less then 1

 

[lanedance]

u know v1 dot v2 = |v1||v2|cos(t), same with v3

In R2, there should only be discrete values for t, how many?

In R3 consider a cone around the vector v1