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Question
Write the value of \[\left( \hat{ i } \times \hat{ j } \right) \cdot \hat{ k } + \left( \hat{ j } + \hat{ k } \right) \cdot \hat{ j } \]
Solution
\[\left( \hat{ i } \times \hat{ j } \right) . \hat{ k } + \left( \hat{ j } + \hat{ k } \right) . \hat{ j } \]
\[ = \hat{ k } . \hat{ k } + \hat{ j } . \hat{ j } + \hat{ k } . \hat{ j } ( \because \hat{ i } \times \hat{ j } = \hat{ k } ) \]
\[ = \left| \hat{ k } \right|^2 + \left| \hat{ j } \right|^2 + 0 ( \because \hat{ k } . \hat{ j } = 0)\]
\[ = 1^2 + 1^2 \]
\[ = 2\]
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