If a plane, intercepts on the coordinates axes at 8,4,4 then the length of the perpendicular from the origin to the plane is

Options

A. `(8)/(3)`
B. `(3)/(8)`
C. 3
D. `(4)/(3)`

Answer

A

Explanation

The required equation of the plane in the intercept form is
`(x)/(8)+(y)/(4)+(z)/(4)=1`
`:.` The distance from orgin to the plane is
`(|0+0+0-1|)/(sqrt(((1)/(8))^(2)+((1)/(4))^(2)+((1)/(4)))),(1)/((1)/(4)sqrt((1)/(4)+1+1))=(4)/(sqrt((9)/(4)))=(8)/(3)`