The length of the normal from origin to the plane x + 2y – 2z = 9 is equal to

Question

Question

This question was previously asked in

NDA (Held On: 10 Sept 2017) Maths Previous Year paper

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Answer 1

Concept:

Perpendicular Distance of a Point from a Plane

Let us consider a plane given by the Cartesian equation, Ax + By + Cz = d

And a point whose coordinate is, (x₁, y₁, z₁)

Now, distance =

Calculation:

We know that normal is always perpendicular to the plane,

Given: Equation of the plane is x + 2y – 2z = 9

⇒ x + 2y – 2z - 9 = 0

Now we have to find the distance from the origin (0, 0, 0)

We know that distance =

∴ Distance =