Consider the line \[ \vec{r} = (\hat{i} - 2\hat{j} + 4\hat{k}) + \lambda(-\hat{i} + 2\hat{j} - 4\hat{k}) \]
Match List-I with List-II:
| List-I | List-II |
|---|---|
| (A) A point on the given line | (I) \(\left(-\tfrac{1}{\sqrt{21}}, \tfrac{2}{\sqrt{21}}, -\tfrac{4}{\sqrt{21}}\right)\) |
| (B) Direction ratios of the line | (II) (4, -2, -2) |
| (C) Direction cosines of the line | (III) (1, -2, 4) |
| (D) Direction ratios of a line perpendicular to given line | (IV) (-1, 2, -4) |