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

• \[10 \hat{ i } + 2 \hat{ j }  + 11 \hat{ k } \]

• \[10 \hat{ i }  + 3 \hat{ j }  + 11 \hat{ k } \]

• \[10 \hat{ i } - 3 \hat{ j }  + 11 \hat{ k } \]

• \[10 \hat{ i }  - 2 \hat{ j }  - 10 \hat{ k } \]

Answer 1

\[\vec{a} \times \vec{b} = \begin{vmatrix}\hat{ i }  & \hat{ j }  & \hat{ k }  \\ 2 & - 3 & - 1 \\ 1 & 4 & - 2\end{vmatrix}\]

\[ = 10 \hat{ i } + 3 \hat{ j }  + 11 \hat{ k } \]