# Line of Intersection of 3 planes

1. Jun 10, 2008

### mikee

1. The problem statement, all variables and given/known dataSolve the following systems and interpret the result geometrically
3x + 4y + 5z - 18 = 0
2x - y + 8z - 13 = 0
-x + 17y + 25z + 11 = 0

2. Relevant equations

3. The attempt at a solution Ive been working on this problem for a while, The first thing i did was find if the vectors are coplanar by V1 . V2xV3 and they are not and then i checked there to see if they were parralel and neither are parralel to the other, so therefore there should be a point of intersection right? But i tryed solve it over and over again but i couldnt come up with a solution, that is could not find x,y and z that satifies all 3 equations which therefore means there is no solution and no point of intersection? am i doing somthing wrong or is this question faulty.

2. Jun 10, 2008

### tiny-tim

Hi there mikee!

Three planes can intersect in a line …

take any two of the given planes, and fine their common line.

Then check to see if that line happens to be on the third plane.