1. The problem statement, all variables and given/known data Find all unit vectors in R4 making an angle of [itex]\pi/3[/itex] with the three vectors A=(1,1,-1,-1) B=(1,-1,1,-1) C=(1,-1,-1,1) 2. Relevant equations u.v=|u||v|cos[itex]\Theta[/itex] 3. The attempt at a solution using V=(w,x,y,z) as the vector we are trying to find, I solved the above equation for all three vectors A,B and C obtaining simultaneous equations to solve, however I obtained x=y=z and w2-wx-x2=0 I am not sure how to solve this to find all unit vectors. Also is there a method of doing this that I am unaware of?