Given \(|\vec a\times\vec b|=\vec a.\vec b\).
Let the angle between vectors \(\vec a\) and \(\vec b\) be θ.
We know the cross product of two vectors \(\vec a\) and \(\vec b\) forming an angle θ is
where \(\hat n\) is a unit vector perpendicular to \(\vec a\) and \(\vec b\)
We also have the dot product of two vectors \(\vec a\) and \(\vec b\) forming an angle θ is
Thus, the angle between two vectors is \(\cfrac{\pi}4.\)
