效果：

代码： 

<template>
  <div>
    <el-container>
      <el-main>
        <div class="box-card-left">
          <div id="threejs"></div>
          <div>
            判断的前提是两个向量平行
              <el-button @click="judge">开始判断</el-button>{{ textList }}
          </div>
        </div>
      </el-main>
    </el-container>
  </div>
</template>
<script>
// 引入轨道控制器扩展库OrbitControls.js
import { OrbitControls } from "three/examples/jsm/controls/OrbitControls.js";
import { GLTFLoader } from "three/examples/jsm/loaders/GLTFLoader.js";
// 效果制作器
import { EffectComposer } from "three/examples/jsm/postprocessing/EffectComposer.js";
// 渲染通道
import { RenderPass } from "three/examples/jsm/postprocessing/RenderPass.js";
// 发光描边OutlinePass
import { OutlinePass } from "three/examples/jsm/postprocessing/OutlinePass.js";
import {
  CSS2DObject,
  CSS2DRenderer,
} from "three/examples/jsm/renderers/CSS2DRenderer.js";
import TWEEN from "@tweenjs/tween.js";
import {
  CSS3DObject,
  CSS3DSprite,
  CSS3DRenderer,
} from "three/examples/jsm/renderers/CSS3DRenderer.js";
// TextGeometry 是一个附加组件，必须显式导入。 three/examples/jsm/geometries
import { TextGeometry } from "three/examples/jsm/geometries/TextGeometry.js";
// FontLoader 是一个附加组件，必须显式导入。
import { FontLoader } from "three/examples/jsm/loaders/FontLoader.js";
export default {
  data() {
    return {
      scene: null, // 场景对象
      camera: null, // 相机对象
      renderer: null, // 渲染器对象
      a: new this.$three.Vector3(10, 0, 0),
      b: new this.$three.Vector3(15, 0, 0),
      c: new this.$three.Vector3(-20, 0, 0),
      textList:[]
    };
  },
  created() {},
  mounted() {
    this.name = this.$route.query.name;
    this.init();
  },
  methods: {
    goBack() {
      this.$router.go(-1);
    },
    /**
     * 如何判断物体是在人的前方还是后方
     * 思路：借助两个单位向量的点乘结果来判断的；
     */
    init() {
      // 创建场景对象
      this.scene = new this.$three.Scene();
      const axesHelper = new this.$three.AxesHelper(60);
      this.scene.add(axesHelper);
      // 创建相机对象
      this.camera = new this.$three.PerspectiveCamera(60,1,0.01,2000);
      this.camera.position.set(25,25,25);
      this.camera.lookAt(0,0,0);
      let arr = [this.a, this.b, this.c];
      arr.forEach((item,index) => {
        let color = null;
        let name = "";
        if(index == 0) {
          color = 0xffffff;
          name = "A";
        } else if (index == 1) {
          color = 0xffccff;
          name = "B";
        } else {
          color = 0xffffaa;
          name = "C";
        }
        this.createArrow(item, color,name);
      })
      this.css3DRenderer = new CSS3DRenderer();
      this.css3DRenderer.setSize(1000,800);
      this.css3DRenderer.render(this.scene, this.camera);
      this.css3DRenderer.domElement.style.position = 'absolute';
      this.css3DRenderer.domElement.style.top = 0;
      this.css3DRenderer.domElement.style.pointerEvents = 'none';

      window.document.getElementById("threejs").appendChild(this.css3DRenderer.domElement);
      // 创建渲染器对象
      this.renderer = new this.$three.WebGLRenderer();
      this.renderer.setSize(1000,800);
      this.renderer.render(this.scene, this.camera);
      window.document.getElementById("threejs").appendChild(this.renderer.domElement); 
      const controls = new OrbitControls(this.camera, this.renderer.domElement);
        controls.addEventListener("change", () => {
          this.renderer.render(this.scene, this.camera);
        })
        this.renderFun();
    },
    createArrow(dir, color, name) {
      let arrow = new this.$three.ArrowHelper(dir.clone().normalize(), new this.$three.Vector3(0,0,0), dir.length(), color);
      arrow.name = name;
      this.scene.add(arrow);
    },
    renderFun() {
      this.css3DRenderer.render(this.scene, this.camera);
      requestAnimationFrame(this.renderFun); // 一定要设置这一句，否则，不渲染
    },
    judge() {
      let a = this.a.clone().normalize();
      let b = this.b.clone().normalize();
      let c = this.c.clone().normalize();
      let a_dot_b = a.clone().dot(b);
      let a_dot_c = a.clone().dot(c);
      let b_cos = Math.acos(a_dot_b);
      let c_cos = Math.acos(a_dot_c);
      let deg1 = this.$three.MathUtils.radToDeg(b_cos);
      let deg2 = this.$three.MathUtils.radToDeg(c_cos);
      this.textList = [];
      if(deg1 == 0) {
        this.textList.push('a和b同向');
      }
      if(deg2 == 180) {
        this.textList.push('a和c反向');
      }
    }
  },
};
</script>
<style lang="less" scoped>
.box-card-left {
  display: flex;
  align-items: flex-start;
  flex-direction: row;

  width: 100%;

  .box-right {
    img {
      width: 500px;
      user-select: none;
    }
  }
}
</style>