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

Explanation

Equation of plane is `vecr. (3hati - 4hatj+12hatk)=8`
compare `vecr.vecn=p`
Then `vecn=3hati - 4hatj+12hatk, p=8`
`therefore` Length of the perpendicular from the origin to the plane is
`d=(p)/(|vecn|)`
`=(8)/(sqrt(3^(2)+(-4)^(2)+12^(2)))`
`=(8)/(sqrt(9+16+144))`
`=(8)/(sqrt(169))`
`=(8)/(13)` unit.