Calculus and vectors
posted by Anita .
A plane, π, has 3x5z+3=0 as its Cartesian equation. Determine the Cartesian equation of a plane that is perpendicular to π and contains the point P(2,9,3)

the normal of the given plane is
(3,0,5) which is then the direction of your line
A vector equation of that line is
r = (x,y,z) = (2,9,3) + t(3,0,5) where t is your parameter
x = 2 + 3t > t = (x2)/3
y = 9 + 0t > y = 9
z = 3  5t > t = (z+3)/5
so
(x2)/3 = (z+3)/5 , y = 9