The equation of plane through (−2,3,5) is a(x+2)+b(y−3)+c(z−5)=0 it is perpendicular to 2x+4y+5z=8&3x−2y+3z=5 ‌∴2a+4b+5c=0 ‌3a−2b+3c=0 ‌∴‌
a
|
4
5
−2
3
|
=‌
−b
|
2
5
3
3
|
=‌
c
|
2
4
3
−2
|
‌⇒‌
a
22
=‌
b
9
=‌
c
−16
∴ Equation of plane is ‌22(x+2)+9(y−3)−16(z−5)=0 ‌⇒22x+9y−16z+97=0 ‌‌ Comparing with ‌αx+βy+γx+97=0 ‌‌ We get ‌α+β+γ=22+9−16=15