The plane `2x+3y+4z=1` meets the coordinate axis in A, B, C. The centroid of the `DeltaABC` is

Options

A. `(2,3,4)`
B. `((1)/(2),(1)/(3),(1)/(4))`
C. `((1)/(6),(1)/(9),(1)/(12))`
D. `((1)/(2),(3)/(3),(3)/(4))`

Answer

C

Explanation

Given plane can be rewritten as
`(2x)/(1)+(3y)/(1)+(4z)/(1)=1`
`rArr" "(x)/(1/2)+(y)/(1/3)+(z)/(1/4)=1`

Since, the plane meets the cossdinate axes at
`A((1)/(2),0,0)B(0,(1)/(3),0)andC(0,0,(1)/(4))`
then, centroid of the `DeltaABC`
`(((1)/(2)+0+0)/(3),(0+(1)/(3)+0)/(3),(0+0+(1)/(4))/(3))`
`=((1)/(6),(1)/(9),(1)/(12))`