Find the vector equation of the line passing through $(1, 2, 3)$ and parallel to the planes $\hat{r}. (\hat{i} - \hat{j} + 2\hat{k}) = 5$ and $\hat{r} (3\hat{i} + \hat{j} + \hat{k} ) = 6$

Question

$\begin{array}{1 1}(A) \overrightarrow r = \hat i + 2\hat j + 3\hat k + \lambda (3\hat i - 5\hat j - 4\hat k ) \\(B) \overrightarrow r = \hat i + 2\hat j + 3\hat k + \lambda (-3\hat i - 5\hat j - 4\hat k ) \\ (C) \overrightarrow r = \hat i + 2\hat j + 3\hat k + \lambda (-3\hat i + 5\hat j - 4\hat k ) \\ (D) \overrightarrow r = \hat i + 2\hat j + 3\hat k + \lambda (3\hat i + 5\hat j + 4\hat k )\end{array} $