1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Intersection of lines

  1. Mar 25, 2017 #1
    1. The problem statement, all variables and given/known data
    For which m and n the lines are concurrent?
    ##r: \begin{cases} x & - & y & = & 1 \\ nx & - & y & - & 2z & + & m & + & 1 & = & 0\end{cases}##

    ##s: \begin{cases} x & - & nz & + & m & + & n & = & 0 \\ x & + & y & - & 2nz & + & 11 & = & 0 \end{cases}##

    Solving r gives me: ##\left(1,0,\frac{m + 1 + n}{2}\right) + y\left(1,1,\frac{n - 1}{2}\right)##

    Solving s gives me: ##(-m - n, n - 11, 0) + z(n, n, 1)##

    For n = -1 or n = 2 the direction vectors are parallel.

    The answer in the book is that for ##n \ne 2## and ##n \ne -1## and ##n + m = 5## the lines are concurrent. However, I've found that for m = 10 and n = 0 the lines intersect at a single point.
     
  2. jcsd
  3. Mar 25, 2017 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I haven't checked your work, but assuming it's correct, I don't see what is bothering you. You know if ##n \ne 2## and ##n \ne -1## the lines are skew in 3D. So they may not intersect or may intersect at a point. So what's the problem?
     
  4. Mar 25, 2017 #3
    I'm trying to reach the condition m + n = 5 for the lines to intersect at a single point. I plugged in some values for m and n such that m + n ≠ 5 and it's true, the lines don't intersect if m + n ≠ 5. However, it seems that m = 10 and n = 0 is an exception.
     
  5. Mar 25, 2017 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    But the problem says if ##m+n=5## the lines are concurrent, i.e., the same line. So why are you trying to show they only intersect at a single point?
     
    Last edited: Mar 25, 2017
  6. Mar 25, 2017 #5

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Also, in your equation for ##s##: ##s = (-m - n, n - 11, 0) + z(n, n, 1)##, that point ##(-m - n, n - 11, 0)## doesn't satisfy the second equation for ##s## so you must have an arithmetic error.
     
  7. Mar 25, 2017 #6
    I'm trying to find for which m the lines intersect and for which m they don't.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted