Let the plane a x+ b y+ c z= d pass through (2,3,-5) and is perpendicular to the planes 2 x+y-5 z=10 and 3 x+5 y-7 z=12. If a, b, c, d are integers d…

Let the plane $\displaystyle \mathrm{a} x+\mathrm{b} y+\mathrm{c} z=\mathrm{d}$ pass through $\displaystyle (2,3,-5)$ and is perpendicular to the planes $\displaystyle 2 x+y-5 z=10$ and $\displaystyle 3 x+5 y-7 z=12$. If a, b, c, d are integers $\displaystyle \mathrm{d}>0$ and $\displaystyle \operatorname{gcd}(|\mathrm{a}|,|\mathrm{b}|,|\mathrm{c}|, \mathrm{d})=1$, then the value of $\displaystyle \mathrm{a}+7 \mathrm{~b}+\mathrm{c}+20 \mathrm{~d}$ is equal to :