[QUE/ME-02017] ME-PROBLEM

 You are given two unit vectors \(\vec{m}=(1,1,1)\) and \(\vec{n}=(1,0,1)\). What should be the unit vector \(\hat{\ell}\) along an axis what should be the angle of rotation \(\alpha\) that will rotate vector \(\vec{n}\) and align it along the vector \(\vec{m}\).

\(\cos\alpha=\frac{\vec{m}\cdot\vec{n}}{|\vec{m}||\vec{n}|}=\frac{1}{\sqrt{3}} \)

Angle \(\alpha\) is given by \(\cos\alpha=\dfrac{\vec{m}\cdot\vec{n}}{|\vec{m}||\vec{n}|}=\dfrac{1}{\sqrt{3}} \);Clockwise rotation by \(\alpha \) about  axis along \(\hat{\ell}=\dfrac{\vec{m}\times\vec{n}}{|\vec{m}||\vec{n}|}= \frac{1}{\sqrt{2}}(1,0,-1)\);