A plane meets the coordinate axes at A, B and C respectively such that the centroid of `Delta`ABC is (1 -2, 3). Find the equation of the plane.

Options

A. `x+2y+3z=1`
B. `3x+2y+z=3`
C. `2x+3y+6z=18`
D. `6x+3y+2z=18`

Answer

D

Explanation

The plane passes through the point A(3,0,0),B(0,6,0) and (C(0,0,9). So, it should satisfy the equation given in option for all the three points.
For point A(3,0,0)
`x+2y+3z=1`
`rArr 3+0+0 ne 1` ltbRgt `:.` option (a) is wrong.
From option(b)
For point A(3,0,0)
`3x+2y+z=3`
`:.3(3)+0+0 ne 3`
`:.` option (b) is wrong.
From option (c)
For point A(3,0,0)
`2x+3y+6z=18`
`:. 2(3)+0+0 ne 18`
`:.` option (c) is worng.
Form option (d)
For point B(0,6,0)
`6x+3y+2z=18`
`rArr 6(3)+0+0=18`
For point C(0,0,9)
`6x+3y+2z=18`
`0+0+2xx9=18`
`:.` Option (d) is correct.