The equation of the plane passing through the point (1, 2, - 3) and perpendicular to the planes 3x + y – 2z = 5 and 2x – 5y – z = 7, is :

Normal vector of required plane is$\overrightarrow{n}=\left|\begin{array}{ccc}\widehat{i}& \widehat{j}& \widehat{k}\\ 3& 1& -2\\ 2& -5& -1\end{array}\right|=-11\widehat{i}-\widehat{j}-17\widehat{k}$

Therefore, the equation of the plane is 11 (x – 1) + (y – 2) + 17 (z + 3) = 0, it implies 11x + y + 17z + 38 = 0