Here is my work, I think its done, although, my professor sent us a list without answers, as usual haha.
It gives 2 lines: πβ1 = β©3 β π‘; 4 + 4π‘; 1 + 2π‘βͺ and πβ2 = β©π‘; 3; 2π‘βͺ.
First I determined that the second line I'm using the parameter (s) instead of t.
After that, I wrote my distance as d=sqr (3ts)Β²+(4+4t3)Β²+(2+2t2s)Β²
I changed to dΒ², cause it will still be the smaller distance.
Ok, 2n I did the partials for d/dt=0 and d/ds=0
3rd n 4th are the answers for dt, dtt, dts, ds, dss, dst.
5th I have done the system, used gauss. I've checked it all on symbolab.
Got t and s. t=1/24 and s=11/8.
Applied s and t on dΒ².
dΒ²= [(3ts)Β²+(4+4t3)Β²+(2+2t2s)Β²]
dΒ²= [(3(1/24)(11/8))Β²+(4+4(1/24)3)Β²+(2+2(1/24)2(11/8))Β²
Got, 109/6 u.d.
Tested by D= dss dst  and gave me 42036= 384. So I have that D>0 and Dtt >0, that should be exactly the point of the smaller distance at relative minimum.
 dts dtt 
Does anyone see any flaws? Thanks.
(some notes in my language, nothing important, just saying what I'm doing so I can study the steps, just like I did here in english)
It gives 2 lines: πβ1 = β©3 β π‘; 4 + 4π‘; 1 + 2π‘βͺ and πβ2 = β©π‘; 3; 2π‘βͺ.
First I determined that the second line I'm using the parameter (s) instead of t.
After that, I wrote my distance as d=sqr (3ts)Β²+(4+4t3)Β²+(2+2t2s)Β²
I changed to dΒ², cause it will still be the smaller distance.
Ok, 2n I did the partials for d/dt=0 and d/ds=0
3rd n 4th are the answers for dt, dtt, dts, ds, dss, dst.
5th I have done the system, used gauss. I've checked it all on symbolab.
Got t and s. t=1/24 and s=11/8.
Applied s and t on dΒ².
dΒ²= [(3ts)Β²+(4+4t3)Β²+(2+2t2s)Β²]
dΒ²= [(3(1/24)(11/8))Β²+(4+4(1/24)3)Β²+(2+2(1/24)2(11/8))Β²
Got, 109/6 u.d.
Tested by D= dss dst  and gave me 42036= 384. So I have that D>0 and Dtt >0, that should be exactly the point of the smaller distance at relative minimum.
 dts dtt 
Does anyone see any flaws? Thanks.
(some notes in my language, nothing important, just saying what I'm doing so I can study the steps, just like I did here in english)
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