Eaton Corp. of Cleveland will close its Salem, Va., plant during the next 2 1/2 years, meaning the eventual loss of 350 jobs, a company spokesman announced. The plant produces electric motors, motorized hand trucks and lift trucks.

Harvey Hincker, general plant manager, said a small number of the employes may be offered transfers to company plants in Greenville and Lenoir, N.C.

Hincker said the company's truck division will become a separate company this year, which leaves the Salem and North Carolina plants with projected overcapacity problems.

The company forecast that only 60 percent of all three plants' capacity would be used during the next five years if all plants remained open.

Corning Glass Works will close its plant in Blacksburg, Va., by mid-1984, leaving 270 people without jobs, the company said.

Eric Birch, general manager of the company's technical products division, said last week that the plant will begin to phase down operations this fall.

Birch said the 343,000-square-foot production facility has not been profitable. He said the products produced at the plant are being hit by a shrinking market.

The plant produces flat glass for a variety of industrial uses, including oven windows, woodstove windows and other smooth-glass cooking products.

Gerald Young, the plant manager, said the facility will operate normally until the final shutdown next year.