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

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(Note: This question has been split into 2 questions) This question appeared in 65-1,65-2 and 65-3 versions of the paper in 2013.