Question

Define vector product of two vectors.

 

Answer 1

\[\text{ If }  \vec{a} \text{ and }  \vec{b} \text{ are two non-zero non-parallel vectors, then the vector product denoted by }  \vec{a} \times \vec{b} \text{ is defined as } \vec{a} \times \vec{b} = \left| \vec{a} \right| \left| \vec{b} \right| \sin \theta \hat{ η }  . \]
\[ \text{ Here } ,\theta \text{ is the angle between } \vec{a} \text{ and } \vec{b} \text{ and } \hat{ η } \text{ is the unit vector perpendicular to the plane of } \vec{a} \text{ and } \vec{b} \text{ such that }  \vec{a} , \vec{b} \text{ and }  \hat{ η } \text{ form a right handed system. } \]