Find all values of k for which the two lines do not interesct Line 1 $r=(2,-1,3)+t(1,0,2)$ Line 2 $r=(2,1,4)+s(2,k,6)$
2026-04-02 21:34:20.1775165660
Vectors intersection question
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It is more straightforward to find the values of $k$ for which the lines do intersect.
You have two parameterised lines $t \mapsto l_1(t), t \mapsto l_2(t)$ and you want to find $s,t $ such that $l_1(s) = l_2(t)$.
Write out the three equations. Two of the equations do not involve $k$ and can be used to solve for $s,t$. Using these values, find the $k$ for which the lines intersect.