Find the equation of the plane passing through the line of intersection of the planes 2x - y = 0 and 3z - y = 0, and perpendicular to the plane 4x + 5y - 3z = 9.
Equation of plane through the line of intersection of planes in Cartesian form is
(1)
For the standard equation of planes,
So, putting in equation (1), we have
2x-y + λ(3z-y)=0
2x + (-1-λ)y + 3λz=0 (2)
Now as the plane is perpendicular the given plane,
For θ=90°, cos90°=0
(3)
On comparing with standard equations in Cartesian form,
Putting values in equation(3),
2.4 + (-1-λ).5 + 3λ.-3=0
8-5-5λ-9λ=0
-14λ=-3
Putting in equation(2)
28x-17y + 9z=0
So, required equation of plane is 28x-17y + 9z=0.