Question

Write the value of \[\left( \hat{ i }  \times \hat{ j }  \right) \cdot \hat{ k }  + \left( \hat{ j } + \hat{ k }  \right) \cdot \hat{ j } \]

 

Answer 1

\[\left( \hat{ i }  \times \hat{ j }  \right) . \hat{ k }  + \left( \hat{ j }  + \hat{ k }  \right) . \hat{ j }  \]
\[ = \hat{ k } . \hat{ k }  + \hat{  j }  . \hat{ j }  + \hat{ k }  . \hat{ j }  ( \because \hat{ i }  \times \hat{ j } = \hat{ k }  ) \]
\[ = \left| \hat{ k }  \right|^2 + \left| \hat{ j }  \right|^2 + 0 ( \because \hat{ k }  . \hat{ j }  = 0)\]
\[ = 1^2 + 1^2 \]
\[ = 2\]