How to render bootstrap rotation with vue

example of bootstrap official website rotation:

<div id="carouselExampleControls" class="carousel slide" data-ride="carousel">
  <div class="carousel-inner">
    <div class="carousel-item active">
      <img class="d-block w-100" src=".../800x400?auto=yes&bg=777&fg=555&text=First slide" alt="First slide">
    </div>
    <div class="carousel-item">
      <img class="d-block w-100" src=".../800x400?auto=yes&bg=666&fg=444&text=Second slide" alt="Second slide">
    </div>
    <div class="carousel-item">
      <img class="d-block w-100" src=".../800x400?auto=yes&bg=555&fg=333&text=Third slide" alt="Third slide">
    </div>
  </div>
  <a class="carousel-control-prev" href="-sharpcarouselExampleControls" role="button" data-slide="prev">
    <span class="carousel-control-prev-icon" aria-hidden="true"></span>
    <span class="sr-only">Previous</span>
  </a>
  <a class="carousel-control-next" href="-sharpcarouselExampleControls" role="button" data-slide="next">
    <span class="carousel-control-next-icon" aria-hidden="true"></span>
    <span class="sr-only">Next</span>
  </a>
</div>

Note that the class activated by carousel-item is crousel-item active

<div id="carouselExampleControls" class="carousel slide" data-ride="carousel">
  <div class="carousel-inner">

    <div class="carousel-item active" v-for="item of data" :key="item.key">
      <img class="d-block w-100" :src="item.key" alt="First slide">
    </div>

  </div>
  <a class="carousel-control-prev" href="-sharpcarouselExampleControls" role="button" data-slide="prev">
    <span class="carousel-control-prev-icon" aria-hidden="true"></span>
    <span class="sr-only">Previous</span>
  </a>
  <a class="carousel-control-next" href="-sharpcarouselExampleControls" role="button" data-slide="next">
    <span class="carousel-control-next-icon" aria-hidden="true"></span>
    <span class="sr-only">Next</span>
  </a>
</div>

this will lead to problems. All class has active, and all of them are active, so you can"t switch between rosters

I think it is written like this

<div id="carouselExampleControls" class="carousel slide" data-ride="carousel">
  <div class="carousel-inner">
    
    <div v-for="(item,index) of data">
    <div v-if="index==0">
        <div class="carousel-item active" :key="item.key">
          <img class="d-block w-100" src="item.img" alt="First slide">
        </div>
    </div>
    <div v-else>
       <div class="carousel-item " :key="item.key">
          <img class="d-block w-100" src="item.img" alt="First slide">
        </div>
    </div>
    
    
  </div>
  <a class="carousel-control-prev" href="-sharpcarouselExampleControls" role="button" data-slide="prev">
    <span class="carousel-control-prev-icon" aria-hidden="true"></span>
    <span class="sr-only">Previous</span>
  </a>
  <a class="carousel-control-next" href="-sharpcarouselExampleControls" role="button" data-slide="next">
    <span class="carousel-control-next-icon" aria-hidden="true"></span>
    <span class="sr-only">Next</span>
  </a>
</div>

but these writes can not be switched, how to solve this?