List of top Higher Mathematics Questions on 3D Geometry

Find the shortest distance between parallel lines: \[ \vec{r_1} = \hat{i} + 2 \hat{j} - 4 \hat{k} + \lambda (2 \hat{i} + 3 \hat{j} + 6 \hat{k}) \,\,\, \text{and} \,\,\, \vec{r_2} = 3 \hat{i} + 3 \hat{j} - 5 \hat{k} + \mu (2 \hat{i} + 3 \hat{j} + 6 \hat{k}) \]

Find the shortest distance between the lines: \[ \vec{r_1} = (1 - t) \hat{i} + (t - 2) \hat{j} + (3 - 2t) \hat{k} \,\,\, \text{and} \,\,\,\vec{r_2} = (s + 1) \hat{i} + (2s - 1) \hat{j} - (2s + 1) \hat{k} \]