Question

The value of  \[\hat{ i }  \cdot \left( \hat{ j }  \times \hat{ k }  \right) + \hat{ j }  \cdot \left( \hat{ i }  \times \hat{ k }  \right) + \hat{ k }  \cdot \left( \hat{ i }  \times \hat{ j }  \right),\]  is 

विकल्प

• 0

• -1

• 1

• 3

Answer 1

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