Continuity mistake: In the original 1980 version, in the first wideshot of Darth Vader's Star Destroyer, the light of a Star Destroyer can be seen on the right side just flying through space. This is fixed in the 2004 DVD release.
Star Wars: Episode V - The Empire Strikes Back (1980)
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Directed by: Irvin Kershner
Starring: Harrison Ford, Frank Oz, James Earl Jones, Mark Hamill, Alec Guinness, Carrie Fisher, Anthony Daniels, Billy Dee Williams, Kenny Baker, Peter Mayhew, David Prowse
Genres: Action, Adventure, Fantasy, Sci-fi, Star Wars, Thriller
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Question: Is there any reason why Luke believes what Darth Vader says when he tells him that he is his father?
Answer: The vision Luke sees in the cave on Dagobah is a clue to this. Luke is realizing he has a lot more in common with Darth Vader than the idealized father he'd always imagined. When Vader tells him he's his father, Luke doesn't want to believe it, but he simply can't deny that it feels much more true that his father would be someone passionate and reckless like himself rather than someone who exemplifies a noble Jedi, which feels like an obvious myth in hindsight.
Chosen answer: He "searched his feelings" as Vader instructed; he reached out with the Force and felt the truth of the statement.
Phixius ★