SomethingStarWarsRelated said:

Watching this “your mother” scene several times lately and noticed something that hadn’t dawned on me before:

Vader: conduct your search and bring his companions to me

Then no search is ever shown. It doesn’t affect the plot. Just a throw away line that doesn’t matter. Shame.

There is no need to show the search, we know it’s happening, and it would just slow down the movie.
And it is not a throw away line. It gives the audience information that Vader is not effected by Luke’s presence, he is still cold and calculating, and we need to see Luke reaction as he realizes that.