If $|\vec{A}| = 2$ and $|\vec{B}| = 4$,then match the relation in Column-$I$ with the angle $\theta$ between $\vec{A}$ and $\vec{B}$ in Column-$II$.
Column-$I$ Column-$II$
$(a) |\vec{A} \times \vec{B}| = 0$ $(i) \theta = 30^{\circ}$
$(b) |\vec{A} \times \vec{B}| = 8$ $(ii) \theta = 45^{\circ}$
$(c) |\vec{A} \times \vec{B}| = 4$ $(iii) \theta = 90^{\circ}$
$(d) |\vec{A} \times \vec{B}| = 4\sqrt{2}$ $(iv) \theta = 0^{\circ}$

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(A-IV, B-III, C-I, D-II) Given $|\vec{A}| = 2$ and $|\vec{B}| = 4$. The magnitude of the cross product is given by $|\vec{A} \times \vec{B}| = |\vec{A}| |\vec{B}| \sin \theta = 8 \sin \theta$.
$(a) |\vec{A} \times \vec{B}| = 8 \sin \theta = 0 \implies \sin \theta = 0 \implies \theta = 0^{\circ}$. Matches with $(iv)$.
$(b) |\vec{A} \times \vec{B}| = 8 \sin \theta = 8 \implies \sin \theta = 1 \implies \theta = 90^{\circ}$. Matches with $(iii)$.
$(c) |\vec{A} \times \vec{B}| = 8 \sin \theta = 4 \implies \sin \theta = 1/2 \implies \theta = 30^{\circ}$. Matches with $(i)$.
$(d) |\vec{A} \times \vec{B}| = 8 \sin \theta = 4\sqrt{2} \implies \sin \theta = 1/\sqrt{2} \implies \theta = 45^{\circ}$. Matches with $(ii)$.

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