Question

If \[\vec{a}\] is a unit vector such that \[\vec{a} \times \hat{ i }  = \hat{ j }  , \text{ find }  \vec{a} . \hat{ i } \] .

 

Answer 1

\[\text{ We know } \]

\[ \hat{ k } \times \hat{ i }  = \hat{ j }            . . . (1)\]

\[\text{ Given } : \vec{a} \times \hat{ i } = \hat{ j }         . . . (2) \]

\[\text{ Comparing (1) and (2), we get} \]

\[ \vec{a} = \hat { k }  \]

\[\text{ Now } ,\]

\[ \vec{a} . \hat{ i } = \hat{ k }  . \hat{ i }  \]

\[ = 0\]