Equation of a plane parallel to a given plane(vector + cartesian)

Equation of plane parallel to a given plane at some distance

The equation of a plane parallel to x-axis is

Find the vector equation of a plane which is parallel to the plane vecr.(2hati-hatj+2hatk)=5 and passes through the point whose position vector is (hati+hatj+hatk) .

Distance of a point from plane (vector + cartesian)

The foot of the perpendicular drawn from the origin to a plane is (4,-2,-5) . Find the equation of the plane in (i) vector form, ii) Cartesian form.

Cartesian plane

Find the vector equation of a plane passing through a point having position vector (2hati-hatj+hatk) and perpendicular to the vector (4hati+2hatj-3hatk) . Also, reduce it to Cartesian form.

Equation of plane (vector and cartesian form) in point normal form

Find the equation of a plane passing through origin and which is perpendicular to a normal vector 2hati+ hatj -hatk . (Cartesian form )