- #1
0kelvin
- 50
- 5
Homework Statement
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.