Equation of pane through point (2,3,−5) and perpendicular to planes 2x+y−5z=10 and 3x+5y−7z=12 is |
x−2
y−3
z+5
2
1
−5
3
5
−7
|=0 ∴ Equation of plane is (x−2)(−7+25)−(y−3) (−14+15)+(z+5)⋅7=0 ∴18x−y+7z+2=0 ⇒18x−y+7z=−2 ∴−18x+y−7z=2 On comparing with ax+by+cz=d where d>0 is a=−18,b=1,c=−7,d=2 ∴a+7b+c+20d=22