[Vuejs]-How to change base url in VUE router?

Your method is also right it should work if there is no other issue,

try with

this.$router.push({ path: '/lang/compare', query: { c: 1,back:1,firstquery:94,queryB:991}})

or you can also try with $router name defining a name on router index file

  {
    path: "/lang/compare",
    name: "compare",
    component: comparePage,
  },

this.$router.push({ name: 'compare', query: { c: 1,back:1,firstquery:94,queryB:991}})