Lou B. Cook, appointed to a three-year term on the school board last week by the Alexandria City Council, said her candidacy for the school board was a "logical extension" of being active in parent-teacher associations for 11 years.

Cook, 42, is a housewife, mother and part-time worker in the Office of Consumer Affairs under the U.S. Department of Health, Education and Welfare.

Formerly a Fairfax County teacher and instructor in Alexandria's homebound program, she is the wife of A. George Cook, Republican and former Alexandria City Councilman.

Cook will replace the Rev. Austin Booker on the school board. Cook received four votes, as Booker, one of three blacks on the board, received two votes in his bid for reappointment.

The six council members who voted on the appointments for the school board unanimously reappointed attorney Micheal Mulroney and school board vice-chairman Alison May. There were 11 candidates for the three positions.

Mayor Mann abstained from voting.

Booker said in an interview that he was "surprised" that he was not reappointed. He said he reapplied only after he was encouraged to do so by the school superintendent and by some council members.

Booker, a school board member since 1973, said, "There would seem to be some racial overtones" in last week's appointments, though he hastened to add he was not making any accusations.He said that adding a new white member to the board when the school population has mor blacks than whites "doesn't seem like we (blacks) are making much progress."

The council last week also made an appointment to the Alexandria Redevelopment and Housing Authority Board, an independent body which oversees public housing and redevelopment in Alexandria.

The new member is Charles R. Hooff III, 37, the controller and manager of his own real estate firm, who will serve four years. He ran for city council as a Republican in 1976 and lost. Hooff will replace Cullen B. Jones, who resigned during a controversy over reorganization of the housing authority.

Last December, the council approved in concept a plan which would make Alexandria City Manager Douglas Harman executive director of the housing authority, replacing current director Harland K. Heumann, who would have become deputy director.

But the housing authority board narrowly rejected the council's plan, instead adopting a compromise proposal which the city manager termed "unworkable" and refused to accept.

Jones was an outspoken opponent of the council's reorganization plan. His replacement, Hooff, said he favors the reorganization. Hooff, one of the seven candidates for the position, was appointed on the second ballot.

Later this year, the council again will have a chance to appoint a new member to the housing authority board. Board chairman A. Melvin Miller has resigned to become an official in the U.S. Department of Housing and Urban Development. Miller was also opposed to the housing authority reorganization. The council voted last week to refer the reorganization issue back to the housing authority.