If vec{a} = 2hat{i} + 2hat{j} - hat{k} and ve | vedclass

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(B) The cross product $\vec{a} 	imes \vec{b}$ is given by the determinant of the matrix formed by the unit vectors and the components of the vectors:

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$\hat{i} - 10\hat{j} - 18\hat{k}$

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(B) The cross product $\vec{a} 	imes \vec{b}$ is given by the determinant of the matrix formed by the unit vectors and the components of the vectors:$\vec{a} 	imes \vec{b} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 2 & 2 & -1 \ 6 & -3 & 2 \end{vmatrix}$Expanding the determinant along the first row:$= \hat{i} ((2)(2) - (-1)(-3)) - \hat{j} ((2)(2) - (-1)(6)) + \hat{k} ((2)(-3) - (2)(6))$$= \hat{i} (4 - 3) - \hat{j} (4 + 6) + \hat{k} (-6 - 12)$$= \hat{i} (1) - \hat{j} (10) + \hat{k} (-18)$$= \hat{i} - 10\hat{j} - 18\hat{k}$

If $\vec{a} = 2\hat{i} + 2\hat{j} - \hat{k}$ and $\vec{b} = 6\hat{i} - 3\hat{j} + 2\hat{k}$,find $\vec{a} \times \vec{b}$.

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