What was Tarkin thinking when Vader said "today will mark the end for the Rebels"?

Near the end of ANH Vader says (referring to that day):
"It has seen the end of Obi-Wan, and it will soon see the end of the Rebel Alliance" (not exact quote).
Tarkin gives Vader a look I'm not quite sure how to interpret. It looks kind of concerned, or thoughtful. We know Tarkin isn't too worried about the Rebel attack, so what was this about?

 

It's like Tarkin is thinking, "Poor Vader...All he has in his life to hold on to is a grudge from 20 years ago, and he actually believes it has relevance to what we are doing today. What a sad sad man".

 

It kinda seems like Tarkin is a bit creeped out with Vader in that scene. I don't really know why, though. Something with Vader's speech or how he worded it. I do know that it has little to do with the attack. As you said, the idea that the rebel attack actually posed a threat to the Death Star never crossed his mind.

 

Seemed to me that Tarkin finds Vaders hate for Obi-Wan a bit creepy. Like: "What on earth made him hate that man so much?"

 

I always interpreted that scene as Tarkin being a bit unconvinced that Kenobi was truly gone.

 

Tarkin was not happy with the strategy of letting the Falcon escape with the rebel plans. The Death Star gave him immunity from rebel attacks, unless the plans revealed a weakness. Putting the Death Star at risk for the hope of destroying one rebel base would not have been his strategy. As a military man, he would have preferred to ensure the safety of the Death Star and then get the rebels at his leasure. (or blow up a planet in retaliation for any rebel attack, forcing them to quit)

However, he dare not stand up to Darth Vader.

 

^^^^^^that

 

He was thinking, "hey when was that line in the movie?"

 

I pretty much agree with Skysoblue, but a simpler explanation may have been it was originally different dialog. Since Vaders mouth doesnt move, it could have been something Tarkin was to react that way too, just a possibility.

 

i think he was just destracted by Yavins beauty and wasnt really paying attention to Vader...

...just a thought

 

It was the Scottish accent. Cushing couldn't understand what David Prowse was saying. Remember it was only later they dubbed Jones' voice.

 

Prowse is English, not Scottish.