Concept:The scalar product of two vectors a and b of magnitude |a| and |b| is given as |a||b| cos ?, where ? represents the angle between the vectors a and b taken in the direction of the vectors.We can express the scalar product as \(\mid\vec a\mid.\mid\vec b\mid\)=|a||b| cos?, where |a| and |b| represent the magnitude of the vectors a and b while cos ? denotes the cosine of the angle between both the vectors and a.b indicates the dot product of the two vectors.Calculation:Given:\(\vec a\) and \(\vec b\) be two unit vectors such that \(|\vec a - \vec b|<2\) and 2? is the angle between \(\vec a\) and \(\vec b\)? \(\mid\vec a\mid= \mid\vec b\mid=1\)We are given \(|\vec a - \vec b|<2.\)Squaring both sides, we get, ? \(|\vec a - \vec b|^2<2^2\)? \((\vec a - \vec b)(\vec a - \vec b)<4\)? \(\mid\vec a\mid^2+ \mid\vec b\mid^2-2\ \vec a.\vec b<4\)? 1 + 1 - 2 \(\mid\vec a\mid. \mid\vec b\mid\ cos2?<4\)? 1 + 1 - 2? . 1 . 1 . cos2? < 4? 2 - 2.cos2? < 4? 1 - cos2? < 2? 2 sin2? < 2? sin2? < 1? - 1 < sin ? < 1 is correct.