Question

Write the value of the area of the parallelogram determined by the vectors   \[2 \hat{ i }  \text{ and } 3 \hat{ j }  .\]

 

Answer 1

\[\text{ Let } :\]
\[ \vec{a} =2 \hat{ i } \]
\[ \vec{b} =3 \hat{ j } \]
\[ \vec{a} \times \vec{b} = 6 \left( \hat{ i }  \times \hat{ j } \right)\]
\[ = 6 \hat{ k } \]
\[\text{ Area of the parallelogram } = \left| \vec{a} \times \vec{b} \right|\]
\[ = 6 \left| \hat{ k }  \right|\]
\[ = 6\left( 1 \right)\]
\[ = 6 \text { sq. units } \]