Find unit vector with a given angle to two other vectors in 3-space 1. The problem statement, all variables and given/known data We are given the vectors <1,0,-1> and <0,1,1>, and are told to find a unit vector that shares an angle of (pi/3) with both of these vectors. 2. Relevant equations a(dot)b = |a||b|cosθ 3. The attempt at a solution So, from the information givin, the only thing I could think to do was form a system of linear equations: u(dot)<1,0,-1> = (√2)cos(pi/3) u(dot)<0,1,1> = (√2)cos(pi/3) u1 - u2 = (.5)(√2) u2 + u3 = (.5)(√2) giving us: u1 = -u3 + (√2) u2 = -u3 + (.5)(√2) so I end up with u = <-u3 + (√2), -u3 + (.5)(√2), u3> u = u3<-1, -1, 1> Now... this is as far away from my answer as I can be! I know it's not right, because this is the equation for a line, not a vector! For informational purposes, the answer in the back of the book is <1/(√2), 1/(√2), 0> How do I get to that answer?