Let \(\vec{\text{a}}\) and \(\vec{\text{b}}\) are two unit vectors such that \(\vec{\text{a}}+2 \vec{\text{b}}\) and \(5\vec{\text{a}}−4\vec{\text{b}}\) are perpendicular. What is the angle between \(\vec{\text{a}}\) and \(\vec{\text{b}}\) ?
1
\(\frac{\pi}{6}\)
2
\(\frac{\pi}{4}\)
3
\(\frac{\pi}{3}\)
4
\(\frac{\pi}{2}\)