The lines r= i- j+l(2 i+ k) and r=2 i- j+m( i+ j- k):

Question

The lines $\vec r=\hat i-\hat j+l(2\hat i+\hat k)$ and $\vec r=2\hat i-\hat j+m(\hat i+\hat j-\hat k)$:

Accepted Answer

Equating components: $1+2l=2+m$, $-1=-1+m\Rightarrow m=0$, $l=-m$. The last two force $m=0,\ l=0$, but then the first equation gives $1=2$, a contradiction. Hence the lines never intersect, for any $l,m$.

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