<s>[INST] Equations of the line which intersects the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{4}$ Find the equations of the line which intersects the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{4}$  and passes through the point $(1,1,1)$.
First I thought required line passes through point on intersection of given lines, but as I checked, lines are non-intersecting. So doesn't that mean that there will be infinite lines which satisfy the given conditions?
 [/INST] write the first equation in the form $$ [x,y,z]=[1,2,3]+t[2,3,4]$$ and the second one in the form $$[x,y,z]=[-2,3,-1]+s[1,2,4]$$
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