What is Ophelia's relationship with her father and brother like in Hamlet?    

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One of the most important scenes of the play toexplore Ophelia's relationship with her father and brother is Act I scene 3, as this scene features a conversation Ophelia has not only with Laertes but also with Polonius, both of them concerning Hamlet and Ophelia's relationship with him. It is clear from the warning that Laertes gives Ophelia, and her response to it, that Ophelia has a deep respect for Laertes that is built on love and a good relationship. Note how he counsels her to be very wary of Hamlet and of getting too close, as he warns her to "fear" the potential consequences of becoming sexually involved with him:

Fear it, Ophelia. Fear it, my dear sister,
And keep you in the rear of your affection,
Out of the shot and danger of desire.
It is clear from what he says that the prime concern of Laertes is his sister's wellbeing, and this shows his love and care for her. Consider especially the way that he refers to Ophelia as "my dear sister," and urges her to keep away from Hamlet for her own good.
This is an attitude that is sharply contrasted with the way that Polonius acts towards his daughter. He demands to be told what she has been talking about with her brother, and then, instead of the gentle, caring advice that Laertes gives, tells her bluntly and openly that if she is not careful she will make both herself and him look like a fool:
Marry, I’ll teach you. Think yourself a baby
That you have ta'en these tenders for true pay,
Which are not sterling. Tender yourself more dearly,
Or—not to crack the wind of the poor phrase,
Running it thus—you’ll tender me a fool.
From the phrasing it is obvious that Polonius is more concerned about his own reputation and standing than he is about what happens to his daughter, which is the complete opposite to the relationship that Laertes has with Ophelia. With one, the relationship is characterised by love and mutual self-regard, but with the other, it is characterised by a power imbalance, as Polonius only cares about Ophelia in relation to his own goals, ambitions, and standing.