Prime Minister-elect Joe Clark, vowing to govern Canada without thrid party support, pledged today to try to unite a country left deeply divided along linguistic lines by the outcome of yesterday's parliamentary elections.

While the swing from the ruling Liberal Party to the Conservatives was strong enough to deal a decisive defeat to Prime Minister Pierre Trudeau, it did not give Clark's party a clear parliamentary majority.

Although it won 136 of the new Parliament's 282 seats, Clark's Progressive-Conservative Party is six seats short of a majority. The Liberals won 114 seats, the socialist New Democratic Party 26 and Social Credit Party 6. Their combined strength could bring down the Clark government at any time.

Clark's Conservatives did not even win a plurality of the popular vote, finishing a half million votes behind the Liberals' 4.5 million, but under Canada's legislative apportionment system, it is seats in Parliament, not the popular vote total, that counts.

The 39-year-old Clark, who will be the youngest prime minister in Canadian history, said today that he hopes he will get a "fair chance" to carry out his mandate. He suggested a conciliatory course that will include frequent consultations with leaders of opposition parties.

"We represent a new team that can bring a new spirit and a new life to out country," he said.

Without a majority, Clark's party could not afford to be overly ambitious and would have to take into account strong opposition by the New Democrats to some of its campaign promises.

Diplomats here expect a "quiet, modest government, plugging along" for at least a year mainly because other parties do not want to force another election and the New Democrats lack funds for another campaign.

Clark, who has started preparations for the takeover, was expected to offer several key Cabinet positions to politicans outside the Conservative Party-an effort to deflect concern about uncertain new leadership facing a national unity crisis dramatized by the election results.

The election has left Canada deeply split along linguistic lines. On its face, the country has become two political territories-one of Liberal Fench Canada and the other of Conservative English Canada, broken by pockets of New Democratic strongholds.

French-speaking Quebec gave Trudeau, a native son, 67 of its 75 seats. Clark got two. Beyond Quebec's borders, French Canadian communities in northern New Brunswick, in St. Boniface, Manitoba, and in eastern and northern Ontario gave Trudeau nearly everything they had.

In contrast, among the 200-odd English-speaking districts outside Quebec, Trudeau won fewer than 40.

Disaffection with Trudeau led to the defeat of 13 English Canadian members of his Cabinet.

As a result, Canada was left practically without a national party and Quebec was left without representation in the new government.

The polarization is taking place as Canada awaits a referendum in which Quebec is to vote whether it wants to become sovereign.

The French-speaking province gave 67 percent of its vote to the Liberals and only 13 percent to the Conservatives. This somewhat lopsided Quebec vote resulted in the Liberals polling more than 4.5 million, or 40 percent, of the national votef the Conservatives just above 4 million, or 36 percent; and the New Democrats more than 2 million or 18 percent of the total.

In his victory speech early today and at a press conference later, Clark pledged himself to form a "truly national government" in which Quebec would have an important voice.

In a gesture aimed at Quebec, Clark suddenly switched to French while speaking from Alberta to a national television audience.

But such gestures and Clark's intentions to ornament his Cabinet with a few French speakers will have to be followed by substantive steps in the coming constitutional negotiations.

Commenting on the election, Quebec Premier Rene Levesque, a leading separatist, said that the outcome showed that the two nations of Canada are now politically identified and that "this polarization may be the start of new talks between" French Canada and English Canada.

In the past Levesque and his separatist colleagues have made the same arguement suggesting that the political division was merely obscured by the presence of a French Canadian prime minister. Some commentators believe the election has strengthened Levesque's appeal for the need to make changes that correspond to political realities.

But the separatists have suffered a series of setbacks in recent weeks including the emergence of differences among their leaders over the referendum that is to be held later this year. Moreover, provincial Liberal leader Claude Ryan has recently emerged as a strong voice for federalism.

While Trudeau was rejected by the country, he was still supported to the end by an overwhelming majority of French Canadians. Clark and English Canada will need him in the coming months to reassure Quebec that it belongs to Canada.

Early this morning, as he conceded defeat, Trudeau reaffirmed his commitment to the Canadian federation in a speech that left little doubt that he intends to fight the separatists. Ironically, Trudeau in defeat seemed to accomplish as much if not more for his dream of national unity than many of his accomplishments in 11 years in power.

Trudeau bowed out gracefully and in the style that had once captured the imagination of Canadians. After a fiery speech to his supporters he ended with a single throw-away line:

"For all its drudgery and broken dreams, the world is still a beautiful place." CAPTION: Picture 1, Canadian Conservative Joe Clark, who toppled Pierre Trudeau, acknowledges his supporters' cheers in Alberta; Picture 2, Pierre Trudeau (Lib: 114 Seats); Picture 3, Joe Clark (P-C: 136 Seats); Picture 4, Ed Broadbent (NDP: 26 Seats); Map, no caption, By Dave Cook-The Washington Post