The foot of the perpendicular drawn from the origin to the plane x + y + z = 3 is

Question

Question

This question was previously asked in

NDA (Held On: 18 Apr 2021) Maths Previous Year paper

Attempt in App

Answer 1

CONCEPT:

Perpendicular distance of a plane ax + by + cz + d = 0 from a point P (x₁, y₁, z₁) is given by:

CALCULATION:

Let A(x, y, z) be the foot of the perpendicular drawn from the origin to the plane x + y + z = 3.

As we know that, the perpendicular distance of a plane ax + by + cz + d = 0 from a point P (x1, y1, z1) is given by:

So, the distance between the origin and the plane x + y + z - 3 = 0 is given by:

So, this means that the length of the line joining the points origin and A is √3

As we can see that from the given options, if A = (1, 1, 1) then the distance between the points origin and A is √3

Hence, correct option is 3.