The Arlington County Board voted unanimously yesterday to go to court in an effort to block the Federal Aviation Administration from testing its controversial "scatter" plan.

The plan is intended to distribute aircraft noise from National Airport more evenly.

The board's vote means that Arlington either will file its own lawsuit in an attempt to stop the test, which is scheduled to begin sometime after September 15, or join forces in court with the Alexandria City Council, which voted Thursday to ask the courts to ban the takeoff and landing test.

FAA officials have said the test could run as long as 90 days.

"We feel Arlington will be significantly impacted by the noise of the scatter plan and have great concerns about noise and the safety of low-altitude turns over heavily populated areas rather than using the river route , which would be safer," Arlington Board member Mary Margaret Whipple said after yesterday's meeting.

Whipple said the board members believe that the plan, which would expose an estimated 350,000 more area residents to jet aircraft noise, should be challenged on the grounds that environmental studies about its effects are "completely inadequate." FAA officials repeatedly have denied this claim.

In a separate, but related vote, the board decided unanimously to oppose a proposal by 17 airlines to increase the ceiling on airliner takeoffs and landings at National Airport from 555 to 605 on weekdays. The board also said that the annual passenger limit at National should be14 million persons. The Transportation Department and the airlines have proposed lowering the passenger ceiling at National from 16 million to 14.8 million. Currently, about13.5 million passengers use the airport each year.

In other action yesterday, the board unanimously approved a plan to build a $23 million retirement home for persons 65 and older, with a built-in "life care" medical unit.

Life care means that the residents in the retirement home are buying the right to live at the complex, with meals and medical care included, until their death. According to the 1980 census, persons over 65 years old account for nearly 12 percent of Arlington's population of 152,000 residents.

The Rosslyn-based Temple Foundation plans to build the facility, to be called Jefferson House, on a two-acre tract bounded by Fairfax Drive, N. Cleveland, N. Barton and a portion of N. 15th streets.

Ken McFarlane Smith, the foundation's attorney, said the plan still must win approval from state health officials for its proposed 74 hospital beds and must apply to the county's industrial development authority for $23 million in industrial revenue bonds in order to build the facility.

The board yesterday also approved a school administration request to spend $265,000 of a$1.2 million school budget surplus on computers, a word-processing system and a cultural arts center at the Hoffman-Boston School. The board decided to put $500,000 in an expense contingency fund for teacher salaries during the fiscal year that begins in July 1984. The rest of the school budget surplus reverts to the county, board members said.