Construction has begun on Vitro Corp.'s new office complex in Rockville, McCormick Construction Co. Inc. Design/Builders has announced. The project will be located on a 24-acre site at the intersection of Maryland Route 355 and West Gude Drive.

A subsidiary of Penn Central Corp., Vitro does most of its work for major defense contracts for the U.S. Navy. The new office complex will serve to consolidate Vitro's operations in the Washington metropolitan area.

Valued at $16.6 million, the complex consists of two, four-story buildings constructed of pre-cast concrete. The two structures comprise more than 239,000 square feet and will be connected by an underground passageway.

Donald N. Coupard Associates has been retained as architect for the project. Work is scheduled to be completed in October 1986.

Other recent developments in commercial realty in the Washington metropolitan area:

* A multimillion-dollar hotel and office complex is being developed in the Westpark section of Tysons Corner by Prospect Co., a wholly owned subsidiary of The Travelers Cos., in a joint venture with Hilton Hotels Corp. and West Group of McLean. Hilton will manage the hotel as well as serve as an equity partner in the joint venture.

The project, consisting of the 450-room McLean Hilton Hotel and a 125,000-square-foot office building, will be built on a 13-acre site on Jones Branch Road adjacent to the Capital Beltway.

Designed by Skidmore, Owings and Merrill Architects of Washington, the office complex is scheduled to be completed next April and to begin operating later in the year. George Hyman Construction Co. of Bethesda is the general contractor.

* Bidnet, a New York general partnership firm specializing in electronic bidding and procurement information, has leased 29,659 square feet of office space at 5 Choke Cherry Rd. in Rockville.

* Quest Research Corp. has leased 14,322 square feet of office space from Planning Research Corp. at the Sterling Systems Building, 1749 Old Meadow Rd., McLean.

* Quest Research Inc. has leased 9,031 square feet of office space feet at the Inglewood Center in Landover.

* E. A. Baker Construction Co. Inc. has been awarded a $3.5 million contract to renovate the Vanderbilt Mansion at 2929 Massachusetts Ave. NW.