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

Explanation

The equation of the plane is
`barr*(3hati - 4hatj + 12hatk) = 8`
This is of the form `barr*barn = 8`, where `barn = 3hati - 4hatj + 12hatk`
`therefore |barn| = sqrt(3^(2) + (-4)^(2) + (12)^(2))`
` = sqrt(9 + 16 + 144) = 13`
The equation `barr*barn=8` can be written as
`barr*(barn)/(|barn|)=(8)/(|barn|)" "i.e, " "barr*((3hati-4hatj+12hatk)/(13))=(8)/(13)`
i.e., `barr*((3)/(13)hati-(4)/(13)hatj+(12)/(13)hatk)=(8)/(13)`
This is the normal forms of the equation of the plane.
`therefore` the length of the perpendicular from the origin to the plane `= (8)/(13)` units.