Could Vader Have Killed Luke?
Vader Does Not Actually Try to Kill Luke, Only Disarm Him, or Dis-Hand Him (Pun Intended) as We See on Bespin's Cloud City. Vader More or Less Wanted to...
Vader does not actually try to kill Luke, only disarm him, or dis-hand him (pun intended) as we see on Bespin's Cloud City. Vader more or less wanted to incapacitate Luke rather than kill him, as is seen in both Empire and Jedi.
Was Vader letting Luke win?
He won because he chipped away at Vader's darkness and took (restored?) his spirit. Luke was a prodigy with the force and a blade, bit he won because Vader loved him and lacked the conviction to really destroy his son.
Why was Vader so weak against Luke?
One, because the second time around Luke knew what he was getting himself into. ... He had no idea what he was dealing with when he went up against Vader, Yoda warned him. Luke was calm and collected in Jedi, something he WAS not when he went up against Vader in Empire.