Line of Intersection of 3 planes

  • Thread starter mikee
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  • #1
mikee
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Homework Statement

Solve the following systems and interpret the result geometrically
3x + 4y + 5z - 18 = 0
2x - y + 8z - 13 = 0
-x + 17y + 25z + 11 = 0




Homework Equations





The Attempt at a Solution

I've 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 couldn't 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.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi there mikee! :smile:

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. :smile:
 

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