The equation of the plane passing through the line of intersection of the planes \( \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1 \) and \( \vec{r} \cdot (2\hat{i} + 3\hat{j} - \hat{k}) + 4 = 0 \) and parallel to the \( x \)-axis is:
\( \vec{r} \cdot (\hat{j} - 3\hat{k}) - 6 = 0 \)
\( \vec{r} \cdot (\hat{i} - 3\hat{k}) + 6 = 0 \)
\( \vec{r} \cdot (\hat{j} - 3\hat{k}) + 6 = 0 \)
\( \vec{r} \cdot (\hat{i} + 3\hat{k}) + 6 = 0 \)
