\(\vec A=\hat i+2\hat j+2\hat k\)
Equation of y-axis is \(\vec y=0\hat i+\hat j + 0\hat k\)
|\(\vec A\)| = \(\sqrt{1+4+4}=3\)
|\(\vec y\)| = \(\sqrt{0+1+0}=1\)
\(\vec A.\vec y=(\hat i+2\hat j+2\hat k).(0\hat i+\hat j+0\hat k)\)
⇒ |\(\vec A\)||\(\vec y\)| cos θ = 2, where θ is angle between \(\vec A\) and y - axis.
⇒ cos θ = \(\frac2{|\vec A||\vec y|}=\frac23\)
⇒ θ = cos-1(2/3) ≈ 48.2°