# Equation of a plane is r(3i−4j+12k)=8. Find the length of the perpendicular from the origin to the plane. - Mathematics and Statistics

Equation of a plane is vecr (3hati-4hatj+12hatk)=8. Find the length of the perpendicular from the origin to the plane.

#### Solution

vecr (3hati-4hatj+12hatk)=8..........(i)

vecn=3hati-4hatj+12hatk

|vecn|=sqrt(9+16+144)=13

therefore vec n=(3 hati-4hatj+12hatk)/13

therefore vecr.((3 hati-4hatj+12hatk)/13)=8/13............ by(i)

vecr.vecn=p

∴ Perpendicular distance from the origin is  8/13

Concept: Plane - Equation of Plane Passing Through the Given Point and Perpendicular to Given Vector
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