Question

A plane meets the coordinate axes at `A ,Ba n dC` respectively such that the centroid of triangle `A B C` is `(1,-2,3)dot` Find the equation of the plane.

Answer 1

`(x/3,y/3,z/3)=(1,-2,3)`
`x/3=1,y/3=-2,z/3=3`
`x=3,y=6,z=9`
`A(3,0,0),B(0,-6,0),C(0,0,9)`
`AB=(-3,-9,0)`
`BC=(0,6,9)`
`AB*BC=|[i,j,k],[-3,-6,0],[0,6,9]|`
`hati(-54)-hatj(-27)+hatk(-18)=0`
`6hati-3hatj+2hatk=0`
`6(x-x_1)+(-3)(y-y_!)+2(z-z_1)=0`
`x_1=3,y_1=0,z_1=0`
`6(x-3)-3y+2z=0`
`6x-3y+2z-18=0`
This is the equation of plane.