Mathematics · JEE | THREE DIMENSIONAL GEOMETRY

The vector equation of the line whose Cartesian equation is \( \frac{x - 5}{3} = \frac{y + 4}{7} = \frac{z - 6}{2} \) is given by:

1. A
   \( \vec{r} = (3\hat{i} + 7\hat{j} + 2\hat{k}) + \lambda(5\hat{i} - 4\hat{j} + 6\hat{k}) \)
2. B
   \( \vec{r} = (5\hat{i} + 4\hat{j} + 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k}) \)
3. C
   \( \vec{r} = (-5\hat{i} + 4\hat{j} - 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k}) \)
4. D
   \( \vec{r} = (5\hat{i} - 4\hat{j} + 6\hat{k}) + \lambda(3\hat{i} + 7\hat{j} + 2\hat{k}) \)