According to edward hall, if you were having a conversation with a lab partner outside science class, the "distance zone" you would share is distance.

Edward Hall said that the “distance zone” that should be shared between you and your lab partner outside the Science Laboratory is personal distance zone.  It was Edward Hall who developed the concept of ‘Proxemics”. He was the American anthropologist whose research focused about how we divide our personal distance and how it’s affected by culture. He also stated the difference between personal space and territory. Furthermore, a conclusion by him was made about the direct correlation between social standings and physical distances between people. He introduced the four main zones which serve as ‘reaction bubbles’. He said that when you enter a specific zone of a person, the person’s psychological and physical reactions will be activated.   

i dont know this man

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."