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Question
If \[\vec{a}\] is a unit vector such that \[\vec{a} \times \hat{ i } = \hat{ j } , \text{ find } \vec{a} . \hat{ i } \] .
Solution
\[\text{ We know } \]
\[ \hat{ k } \times \hat{ i } = \hat{ j } . . . (1)\]
\[\text{ Given } : \vec{a} \times \hat{ i } = \hat{ j } . . . (2) \]
\[\text{ Comparing (1) and (2), we get} \]
\[ \vec{a} = \hat { k } \]
\[\text{ Now } ,\]
\[ \vec{a} . \hat{ i } = \hat{ k } . \hat{ i } \]
\[ = 0\]
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