using UnityEngine;

using System.Collections;

public class PlayerScript : MonoBehaviour {

    public GameObject cameraObject;

    public float cameraDistance;//the distance the camera should be palced from the palyer

    public float cameraHeight;//how heigh the camera should be

    private float cameraAngleToPlayer;// the current angle the camera is to the palyer

    private Vector3 tempVector; // the temporary vector we shall use for calcuations

    // Use this for initialization

    void Start () {

    }

    // Update is called once per frame

    void Update () {

        tempVector = Vector3.left;

        if(Input.GetKey ("left")) //rotation the angle based on input

        {

            cameraAngleToPlayer = cameraAngleToPlayer - (Time.deltaTime * 50f);

        }else if(Input.GetKey("right")){

            cameraAngleToPlayer = cameraAngleToPlayer +(Time.deltaTime *50f);

        }

        Debug.Log("Quaternion:"+Quaternion.AngleAxis(90f,Vector3.up)+";tempVector:"+tempVector);

        tempVector = Quaternion.AngleAxis(cameraAngleToPlayer,Vector3.up)*tempVector;//We are now rotating the Vector around the vertical(y) axis by an angle specificed in the variable 'cameraAngleToPlayer'

        Debug.Log("tempVector after calculate:"+tempVector);

        Debug.DrawLine(transform.position,tempVector*10f,Color.yellow);

        cameraObject.transform.position = transform.position + (tempVector.normalized * cameraDistance) + new Vector3(,cameraHeight,);

        cameraObject.transform.rotation = Quaternion.LookRotation(transform.position - cameraObject.transform.position);

    }

}

以上是绕cube旋转摄像机的示例代码，这段代码拖到cube上。
Quaternion*Vector3的几何意义