Question

in what ratio does the plane {2x+2y-2z=1} divide the line segment joining (2,1,5) and (3,4,3)

Answer 1

let the plane divide the line in the ratio k:1
let (x,y,z) be its co-ordinates,then
(x,y,z)=((3k+2)/(k+1),(4k+1)/(k+1),(3k+5)/(k+1)) respectively
if this point lies on the plane 2x+2y-2z=1,then
2(3k+2)/(K+1)+2(4k+1)/(k+1)-2(3k+5)/(k+1)=1
6k+4+8k+2-6k-10=k+1
6k+8k-6k-k=1-4-2+10
7k=6
k=6/7
Hence ratio is 6/7:1 or6:7

Answer 2

Thanks a lot dude =D
i previously tried the same thing and got a rediculous answer :P
turns out i made an addition mistake :P lol

Answer 3

yw