Find the equation of the plane with normal to the equation x

Find the equation of the plane with normal to the equation x + 2y + 3z = 0 and intersect with point (2, 3, 5).

given the plane equation is x+2y+3z=0

and intersecting point is (2,3,5)

Key point:

A plane with normal vector (n1,n2,n3) has equation

n1 x + n2 y +n3 z= k

for some k.

here (n1,n2,n3) is (1,2,3)

1 x + 2 y + 3 z= k is intersecting at point(2,3,5)

so plug the point to find the value of k

2 +2(3) +3(5) =k

2+6+15 =k

k = 21+2

k=23

the normal form of equation is x+2y+3z = 23