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Let $\vec{a} = 3\hat{i} + 2\hat{j} + x\hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + \hat{k}$, for some real $x$. Then $|\vec{a} \times \vec{b}| = r$ is possible if:
(1) $\sqrt{\frac{3}{2}} < r \leq 3\sqrt{\frac{3}{2}}$
(2) $r \geq 5\sqrt{\frac{3}{2}}$
(3) $0 < r \leq \sqrt{\frac{3}{2}}$
(4) $3\sqrt{\frac{3}{2}} < r < 5\sqrt{\frac{3}{2}}$
BETA
