If \vec{A} = 3\hat{i} + \hat{j} + 2\hat{k} and \(\vec{\mathbf{B}} = 2\hat{i} - 2\hat{j} + 4\hat{k}\) then value of \(\left| \vec{A} \times \vec{B} \right|\) will be
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\(\vec{A} \times \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 3 & 1 & 2 \\ 2 & -2 & 4 \end{vmatrix}\)
\(= (1 \times 4 - 2 \times -2) \hat{i} + (2 \times 2 - 4 \times 3) \hat{j} + (3 \times -2 - 1 \times 2) \hat{k}\)
= 8\hat{i} - 8\hat{j} - 8\hat{k}
\ \ Magnitude of \(\vec{A} \times \vec{B} = \left| \vec{A} \times \vec{B} \right| = \sqrt{(8)^2 + (-8)^2 + (-8)^2}\)
\(= 8 \sqrt{3}\)
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