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Question
Solution
\[\text{ Given } : \]
\[ \vec{a} = 4 \hat{ i } + 3 \hat{ j } + \hat{ k } \]
\[2 \vec{b} = 2 \hat{ i }+ 0 \hat{ j } - 4 \hat{ k } \]
\[2 \vec{b} \times \vec{a} = \begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 2 & 0 & - 4 \\ 4 & 3 & 1\end{vmatrix}\]
\[ = \left( 0 + 12 \right) \hat{ i } - \left( 2 + 16 \right) \hat { j } + \left( 6 - 0 \right) \hat{ k } \]
\[ = 12 \hat{ i } - 18 \hat{ j } + 6 \hat{ k } \]
\[ \Rightarrow \left| 2 \vec{b} \times \vec{a} \right| = \sqrt{{12}^2 + \left( - {18}^2 \right) + 6^2}\]
\[ = \sqrt{504}\]
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