The great vaults of the Washington Cathedral rang with hymns and words of hope in a prayerful and joyous conclusion yesterday to the weeklong National Salute to Vietnam Veterans. The Rev. Theodore H. Evans Jr., in a memorial service, exhorted veterans and all Americans to remember the agony of the war in order "to be whole again . . . that by remembering we may become a living memorial."

"A lot of healing, I think, went on" in the last week, said Jan C. Scruggs, the former combat infantryman who led the effort to build the new national memorial to Vietnam veterans that was dedicated Saturday. " . . . We were hoping that people would react very positively and patriotically to the veterans, and they did . We achieved a kind of collective psychological state: just a real positive and joyous time."

Indeed, if there was a theme for the week, it was that extraordinary outpouring of emotion: an allegiance between men who had walked the jungles of Asia together and who, last week, walked the streets of Washington in their faded fatigues and boonie hats. Rarely in this city have so many men been seen to break down in tears in public, to embrace one another as they remembered a shared past.

In one scene -- similar to scenes repeated a hundred times near the polished, black granite walls of the memorial on Saturday -- a young veteran wearing a buckskin coat recognized a full Army colonel dressed in his uniform.

"I was in your company," said the young man.

"What did you do?" asked the colonel.

"Medic," said the young man. "I was a medic." Then he choked back his tears, and the colonel put a fatherly arm around his shoulder, patting him on the back.

It was not a week of generals, admirals, politicians or defense analysts, but one of ordinary American men and women who once went to fight a war. Scruggs, an enlisted man severely wounded in combat, conceived the memorial and salute. Others who had little rank in the war, along with some former officers, came in groups and singly from around the country, some of them hitchhiking from as far away as Oregon.

As they marched state-by-state down Constitution Avenue in an old-fashioned, patriotic parade before the memorial dedication Saturday, dressed in their faded and irregular uniforms or street clothes, flags snapping in the chill November winds, bands blaring, led by the legless and others in wheelchairs, they called to mind George Washington's crew of ragtag volunteers 200 years ago.

Quint Johnson, a former Green Beret, now an accident investigator for the National Transportation Safety Board, put it this way: "We left from small towns all over the country and went and fought. We found out what it was like . . . and eventually we came back, at least most of us did.

"Then we stuffed the medals and uniforms in some closet or another like we were ashamed and didn't want to be associated with it.

"Well," Johnson went on, "now we're out of that closet. We're brothers, after all. This is our catharsis. This is our moment."

"I have known few times in the history of this cathedral so fraught with emotion and human concern," Canon Charles A. Perry told the 2,200 worshipers who filled the church yesterday, referring to the candlelight vigil at the cathedral that continued for much of the week in which the names were read aloud of all 57,939 dead and missing American soldiers in Vietnam.

Now those names -- each and every one -- are etched in granite on the new memorial. It stands on Washington's Mall occupying some of the nation's most hallowed ground between the shrines to Abraham Lincoln and George Washington.

Last week's salute, which at its peak on Saturday brought an estimated 205,000 veterans, their families and other citizens to Washington, was strongly marked -- as was the war -- by cross-racial understanding and emotion. In the parade down Constitution Avenue, among the throngs of observers at the memorial, and in reunions at smoke-filled hotel lobbies, blacks, whites, Latinos, Asian Americans and American Indians joined together to march, sing, and embrace.

Al (Doc) Allison, a black former Green Beret medic, ecstatic upon seeing a white man at the Sheraton he had mended years ago in the jungles of Vietnam, slapped him five and shouted, "Damn, it good to see you, man."

Bill Menard, a Sioux Indian from South Dakota who was an Army infantryman in the war, joined a small circle of whites and blacks wearing Army fatigues at the memorial and immediately there were enthusiastic hand slaps all around. "Welcome home, brother," they said.

On the Mall, a black man in full combat uniform, with a tree branch stuck in his helmet to complete the camouflage effect, was greeted with hearty slaps on the back and soul handshakes by a group of whites.

Often last week, it seemed as if many of the men had been frozen in time. Friday night, at the Vietnam veterans' dance at the Capital Hilton, many veterans, long-haired and bearded, showed up in faded fatigues, looking almost as if they had not taken them off since the war.

Wolfman Jack, the well-known, gravel-voiced disc jockey of the 1950s and 1960s, was there along with a handful of Congressional Medal of Honor winners--one of whom had a metal hook where his left arm had been. The disc jockey and the award winners grabbed the mike between songs and shouted to the vets that they were heroes, that this was their week at last, and they responded with shouts and cheers. At one point the crowd joined hands to sing "God Bless America."

With the memorial and week of salutes, the organizers set out to honor America's Vietnam veterans and begin a process of reconciliation and healing after this century's most divisive war. To a large extent, they felt yesterday, they succeeded.

Robert W. Doubek, formerly a junior officer in Vietnam who as Scruggs' righthand man supervised and brought off on schedule the construction of the memorial, said he was told repeatedly last week by veterans "that the memorial is a validation for their service, their experience, their sacrifice, their trauma."

For most of the veterans, traveling the parade route on foot and in wheelchairs to the cheers and applause of onlookers, then coming to the walls of the memorial at which some were so moved they reached out and ran their hands over the etched names of their fallen comrades, the week held a measure of satisfaction long denied.

And for many ordinary citizens who came to honor their fighting men, the same could be said: During Saturday's parade, one old man suddenly rushed from the crowd to shake the hand of a legless veteran in a wheelchair; at the memorial, strangers, civilians wearing street clothes, many of them too young to remember Vietnam, approached veterans and simply pumped their hands. Those spontaneous acts, repeated over and over last week, seemed not to glorify war or warriors but to acknowledge a simple need for appreciation.

Yesterday, crowds returned to the memorial. Among them was Herbie Petit, a machinist and former marine from New Orleans. "Last night," he said, standing near the wall, "I went out to dinner with some other ex-marines. There was also a group of college students in the restaurant. We started talking to each other and before we left they stood up and cheered us.

"The whole week," Petit said, his eyes red, "it was worth it just for that."