- #1

elphin

- 18

- 0

**help needed with 3d geometry problem: important!**

## Homework Statement

find the equations of the two planes through the origin which are parallel to the line

(x - 1)/2 = (-y-3) = (-z-1)/2

and at a distance of 5/3 from it. also, show that the planes are perpendicular

## Homework Equations

## The Attempt at a Solution

my attempt at the solution

plane equations passing through (0,0,0) are ax+by+cz=0 (&) a'x+b'y+c'z=0

now, 2.a - b - 2.c = 0 (since direction ratios of given line is perpendicular to the normal of the plane)

also by distance formula (a.(1) + b.(-3) +c.(-1))/(a^2 + b^2 + c^2)^(1/2) = 5/3

the a - 3.b - c = 5/3 (since a^2 + b^2 + c^2 = 1)

and now i am stuck...

FYI : [the answer is 2x+2y+z=0; x-2y+2z=0]