Let the angles between two different unit vectors a = (x1, y1,0), B = (X2, y2,0) and C = (1,1,1) in space be equal to π / 4, and find the values of X1 + Y1 and x1 · Y1

Let the angles between two different unit vectors a = (x1, y1,0), B = (X2, y2,0) and C = (1,1,1) in space be equal to π / 4, and find the values of X1 + Y1 and x1 · Y1

cosπ/4=1/√2=ac/(|a||c|)=(x1+y1)/√3.∴x1+y1=√3/√2
3/2=x1²+2x1y1+y1²=1+2x1y1.2x1y1=1/2.
(x1-y1)²=1-1/2=1/2.∴x1-y1=±1/√2