If a plane meets the coordinate axes at A,B and C such that the centroid of the triangle is (1,2,4) then the equation of the plane is

Options

A. `x+2y+4z=12`
B. `4x+2y+z=12`
C. `x+2y+4z=3`
D. `4x+2y+z=3`

Answer

B

Explanation

Let equation of plane is `x/(alpha)+y/(beta)=z/(gamma)=1` then `A(alpha, 0,0), B(0,beta,0)` and `C(0,0,gamma)` are the points on coordinates axes.
Since, the cenroid of a triangle is (1,2,4).
Now `(alpha)/3=1`
`:. alpha=3,(beta)/3=2impliesbeta=6`
and `(gamma)/3=4impliesgamma=12`
`:.` Equation of plane is
`x/3+y/6+z/12=1`
`implies 4x+2y+z=12`