Question

If   \[\vec{a} \text{ and }  \vec{b}\] are two vectors such that \[\left| \vec{a} \times \vec{b} \right| = \sqrt{3}\text{ and }  \vec{a} . \vec{b} = 1,\]  find the angle between.

 

 

 

Answer 1

\[\left| \vec{a} \times \vec{b} \right| = \sqrt{3}\]

\[ \Rightarrow \left| \vec{a} \right| \left| \vec{b} \right| \sin \theta = \sqrt{3} . . . (1)\]

\[ \vec{a} . \vec{b} = 1\]

\[ \Rightarrow \left| \vec{a} \right| \left| \vec{b} \right| \cos \theta = 1 . . . (2)\]

\[\text{ Dividing (1) by (2), we get } \]

\[\frac{\left| \vec{a} \right| \left| \vec{b} \right| \sin \theta}{\left| \vec{a} \right| \left| \vec{b} \right| \cos \theta} = \sqrt{3}\]

\[ \Rightarrow \tan \theta = \sqrt{3}\]

\[ \Rightarrow \theta = {60}^o \]