In Hamlet, by William Shakespeare, the relationships between the characters in Act One, scene three (with Polonius, Laertes and Ophelia) follow social and familial confines.
In terms of family, the men rule Ophelia's life. This is a society where women are at the mercy of the men in their lives: fathers, husbands, brothers, etc. Polonius as the senior member of the family provides guidance for son and daughter. Laertes, as a male, can also exert control over his sister. Ophelia is left with no options other than to follow the dictates of the male members of her family. She is, more than anything, a commodity or piece of property. The only thing she has of value, according to society—vocalized by her brother—is her untainted virginity.
In terms of the family, the guidelines are very similar. Polonius has authority over both children; Laertes has authority over his sister; and, Ophelia has no power at all.
Polonius' relationship is to Laertes is shown as he provides lengthy advice to his son prior to his departure. (Ironically, Polonius gives excellent advice but fails to follow it himself.) Perhaps the best piece of advice he provides is:
This above all: to thine own self be true,
And it must follow, as the night the day,
Thou canst not then be false to any man. (I.iii.82-84)
Polonius, as the father and senior male, is one with the authority to give direction to his son. Had Polonius followed this advice, he would most probably have avoided not only his own death, but prevented his son's and daughter's deaths as well.
Laertes' relationship to his father is seen in his response to his dad's advice. Laertes responds with appropriate respect.
Most humbly do I take my leave, my lord. (I.iii.86)
Women during this time had no rights. First Laertes, as an older brother, warns his sister to avoid Hamlet because he only wants to lure her to bed: he will never be able to marry her because of their different social status, so Laertes tells Ophelia to guard her virtue (virginity) well.
...weigh what loss your honour may sustain
If with too credent ear you list his songs,
Or lose your heart, or your chaste treasure open
To his unmast'red importunity.
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. (I.iii.32-38)
Ironically, Ophelia reminds her brother that chaste behavior is demanded of him as well. This is something she might only be able to say to her brother. It shows that she has spirit, though the actions of the men around her will eventually take their toll and break her.
Ophelia must also listen to her Polonius' advice, as a father and man. He echoes Laertes' advice, but also draws Ophelia into the deceit he and Claudius use to attempt to ensnare Hamlet, to discover his motivations. Although Polonius and Claudius have different reasons for their use of Ophelia, her power is non-existent in both cases, in face of parent and King, and men, in general.
Polonius reiterates Laertes' advice, cautioning Ophelia to behave with Hamlet or she will lose her virginity, making Polonius look like a fool. Neither brother or father have any real concern for Ophelia's feelings.
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.
The relationships are based on family relationships and societal expectations.