Find the vector equation of the plane passing through the intersection of the planes $\overrightarrow r .(2\hat i + 2 \hat j - 3\hat k) = 7, \overrightarrow r .(2\hat i + 5\hat j + 3\hat k ) = 9$ and through the point $(2, 1, 3).$

Question

$\begin{array}{1 1} \overrightarrow r .(4\hat i + 7\hat j -15\hat k)=30 \\ \overrightarrow r .(4\hat i + 7\hat j -15\hat k)=153 \\ \overrightarrow r .(38\hat i + 68\hat j + 3\hat k)=153 \\ \overrightarrow r .(38\hat i + 68\hat j + 3\hat k)=-153\end{array}$