Let a̅, b̅, and c̅ be three unit vectors such that \(\overline a \times \left( {\overline b \times \overline c } \right) = \frac{1}{{\sqrt 2 }}\left( {\overline b + \overline c } \right)\) and b̅ is not parallel to c̅ . If α and β are the angles between a̅, b̅, and a̅, c̅ respectively then α - β =
1
\(\frac{3\pi}{4}\)
2
\(\frac{\pi}{4}\)
3
\(\frac{\pi}{2}\)
4
0