Posted by Anita on Monday, April 9, 2012 at 3:56am.
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)

Calculus and vectors  Reiny, Monday, April 9, 2012 at 9:10am
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
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