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Find the equation of the plane through the line of intersection of \( \vec{r} \cdot(2 \hat{i}-3 \hat{j}+4 \hat{k})=1 \) and \( \vec{r} \cdot(\hat{i}-\hat{j})+4=0 \) and perpendicular to the plane \( \vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})+8=0 \). Hence, find whether the plane so obtained contains the line \( x-1=2 y-4=3 z-12 \)
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