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Question
If \[\hat{ i } , \hat{ j } , \hat{ k } \] are unit vectors, then
Options
\[\hat{ i } . \hat{ j } = 1 \]
\[\hat{ i } . \hat{ i } = 1 \]
\[\hat{ i } × \hat{ j } = 1 \]
\[\hat{ i } × ( \hat{ j } × \hat{ k} ) = 1 \]
Solution
\[\text{ Let us check each option one by one.} \]
\[(a) \text{ We know } \]
\[ \hat{ i } . \hat{ j } = 0\]
\[ \neq 1\]
\[\]
\[(b) \text{ We know } \]
\[ \hat{ i } . \hat{ i } = \left| \hat{ i } \right|^2 \]
\[ = 1^2 \]
\[ = 1\]
\[(c) \hat{ i } \times \hat{ j } = \hat{ k } \]
\[ \neq 1\]
\[(d) \hat{ i } \times \left( \hat{ j } \times \hat{ k } \right) = \hat{ i } \times \hat{ i } \]
\[ = 0\]
\[ \neq 1\]
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