You should suppose that the plane `x+y+z=8` divides the line segment joining the points A and B at Q(x,y,z) in the ratio k:1, hence, the coordinates of Q point are:
`((2-3k)/(k+1) , (4+5k)/(k+1), (-3+4k)/(k+1))`
Notice that the point lies in the plane x+y+z=8 such that:
`2 - 3k = 4 + 5k = -3 + 4k`
`-2 = 8k =gt k = -1/4 `
`7 = -k =gt k = -7 `
`5 = 7k =gt k = 5/7 `
Hence, the segment joining A and B divides the plane in the ratio 5:7.