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Question
If \[\vec{a} = 2 \hat{ i } - 3 \hat{ j } - \hat{ k } \text{ and } \vec{b} = \hat{ i } + 4 \hat{ j } - 2 \hat{ k
} , \text{ then } \vec{a} \times \vec{b}\] is
Options
\[10 \hat{ i } + 2 \hat{ j } + 11 \hat{ k } \]
\[10 \hat{ i } + 3 \hat{ j } + 11 \hat{ k } \]
\[10 \hat{ i } - 3 \hat{ j } + 11 \hat{ k } \]
\[10 \hat{ i } - 2 \hat{ j } - 10 \hat{ k } \]
Solution
\[\vec{a} \times \vec{b} = \begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 2 & - 3 & - 1 \\ 1 & 4 & - 2\end{vmatrix}\]
\[ = 10 \hat{ i } + 3 \hat{ j } + 11 \hat{ k } \]
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