State True or False for the statements

If the foot of perpendicular drawn from the origin to a plane is (5, – 3, – 2),then the equation of plane is.

False

Let O be the origin, and P be the foot of the perpendicular drawn from the origin to plane

Then, position vector OP will be [which is normal of plane]

Unit vector of n is

Also,

By distance formula, we have distance between two points

A(x₁, y₁, z₁) and B(x₂, y₂, z₂) is

= √38

Now, equation of plane with unit normal vector and having perpendicular distance from origin d is

Equation of given plane is,

Which is given, hence statement is true!