Find the ratio, in which the plane `x + y + z =1/5` divides the line joining the points `(3, 1, 4) and (4, 2,5)`.

Answer

N/a

Explanation

Let the required ratio be k : 1.
Co-ordinates of a point that divides the join of (3, 1, 4) and (4, 2, 5) in the ratio k : 1, are
`((4k+3)/(k+1),(2k+1)/(k+1),(5k+4)/(k+1))`
This point lies on the plane `x+y-z=(1)/(5)`
`therefore (4k+3)/(k+1)+(2k+1)/(k+1)-(5k+4)/(k+1)=(1)/(5)`
`implies 5(4k+3+2k+1-5k-4)=k+1`
`implies 5k=k+1`
`implies k=(1)/(4)`
`therefore` Required ratio = 1 : 4.