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Consider the lines$$L_1:\frac{x+1}{3} = \frac{y+2}{1} = \frac{z+1}{2}$$$$L_1:\frac{x-2}{1} = \frac{y+2}{2} = \frac{z-3}{3}$$
The unit vector perpendicular to both $$L_1$$ and $$L_2$$ is
$$\frac{-\hat{i} + 7\hat{j} + 7\hat{k}}{\sqrt{99}}$$
$$\frac{-\hat{i} - 7\hat{j} + 5\hat{k}}{5\sqrt{3}}$$
$$\frac{-\hat{i} + 7\hat{j} + 5\hat{k}}{5\sqrt{3}}$$
$$\frac{7\hat{i} - 7\hat{j} - \hat{k}}{\sqrt{99}}$$
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