# A plane,`pi` has 3x-5z+3=0 as cartesian equation.Determine the Cartesian equation of plane that is perpendicular to `pi` and contains point P(2,9,-3). b) determine the cartesian equation of a plane...

A plane,`pi` has 3x-5z+3=0 as cartesian equation.Determine the Cartesian equation of plane that is perpendicular to `pi` and contains point P(2,9,-3).

b) determine the cartesian equation of a plane that contains P and is parallel to `pi`

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for finding a plane perpendicular to the given plane we need two points

solution to the bit b)

given the plane is parallel to 3x-5z+3 = 0

this can be written az 3x-5z = -3

as the planes are parallel the equation of required plane is 3x-5z+k = 0, where k is a constant.................(1)

as the plane has the point (x,y,z) = (2,9,-3)

plug in x= 2, y=9 and z= -3 in equation (1) and simplify for k

we have 3x-5z+k = 0

3*2 - 5*-3 + k= 0

6+15+k=0

21+k = 0

so k= -21, plug in k in equation (1)

thus the cartesian equation of the plane is 3x-5z-21 = 0