LOOK FOR (искать): look for a job; look for a new apartment; look for a place to live; look for a nice hotel to stay; look for a book; look for an answer; look for advice; look for help; she is looking for her keys; he is looking for a way to solve this problem; I'm looking for Mr. Smith; I'm looking for black leather shoes in size 8; I'm looking for Oak Street; they are looking for excitement; they are looking for trouble; What are you looking for? What qualities are you looking for in your friends?
SEARCH (искать, обыскать): search for truth; search for beauty; search for peace of mind; search for gold; search for a book; search for an answer; he searched his mind for an explanation, but couldn't find any; he searched his memory but couldn't remember her name; he searched her face for a clue; she searched her apartment for the lost ring; the police searched the house; the police searched the suspects for hidden weapons; Search me!
SEEK (formal: искать, пытаться найти): seek the truth; seek help; seek advice; seek someone's approval; seek employment; seek work; seek fame; seek wealth; seek one's fortune; seek protection; seek a way to solve the problem; seek shelter; seek a place for rest; seek for gold; seek for peace of mind; seek and ye shall find; be sought after; experienced managers are much sought after by employers.