Find the vector equation of the line passing through \( (1,2,3) \) and parallel to the planes \(...

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