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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

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

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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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