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Find the distance of the plane 2x-y+2z+1...

Find the distance of the plane `2x-y+2z+1=0` from the origin.

Text Solution

Verified by Experts

The plane can be put in vector form as `vecr*(2hati-hatj-2hatk)=9`, where `vecr=2hati-hatj-2hatk`. Here
`" "vecn=2hati-hatj-2hatk`
`rArr" "(vecn)/(|vecn|)=(2hati-hatj-2hatk)/(3)`
Dividing equation throughout by 3, we have equation of plane in the normal form as
`" "vecr*((2hati-hatj-2hatk))/(3)=3,`
in which 3 is the distance of the plane from the origin.
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