Find the angle between two lines

Line 1: x=y, z=0
Line 2: x=z, y=0

..............z
.x=z,y=0..|
..........\....|
............\..|
..............\|________y
............./..\
.........../......\
........./..........\
.......x.........x=y, z=0

x=y, z=0 I will use the vector a=1i+1j+0k
x=z, y=0 I will use the vector b=1i+0j+1k

cos Θ= a∙b/ (||a||∙||b||)
cos Θ = (1,1,0)∙(1,0,1) / [√(1²+1²+0²)√(1²+0²+1²)]
cos Θ = 1+0+0 / [√2√2]
cos Θ = 1/2
Θ= π/3 = 1.047 rad = 60°