Question

The perpendicular distance of the plane `barr.(2hati +3hatj-hatk)=5`, from the origin is ______.

Options

• `5/sqrt14` units

• `5/14` units

• 5 units

• `sqrt14/5` units

Answer 1

The perpendicular distance of the plane `barr.(2hati +3hatj-hatk)=5`, from the origin is `bbunderline(5/sqrt14units)`.

Explanation:

Comparing `barr.(2hati +3hatj-hatk)=5` with `barr.barn=p`, we get

`barn=2hati +3hatj-hatk` and p = 5

Length of the perpendicular from the origin to the plane = `p/|n|`

= `5/sqrt(2^2+3^2+(-1))`

= `5/sqrt(4+9+1)`

= `5/sqrt14` units