Word Count : 245

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To find the cross product \(\vec{a} \times \vec{b}\) where \[ \vec{a} = 2\hat{i} + 3\hat{j} + 4\hat{k} \] and \[ \vec{b} = 3\hat{i} + 5\hat{j} + 2\hat{k} \] we can use the determinant of a matrix formed by the unit vectors \(\hat{i}, \hat{j}, \hat{k}\) and the components of \(\vec{a}\) and \(\vec{b}\). The cross product is given by: \[ \vec{a} \times \vec{b} ____ ______ _______ ________ ______ ___ _________ ________ __________ ___ ________.
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