Make camera move and look at an object over time

Hi all,

I need a script which moves a camera from the player towards an item. I want this to be achieved over time using a Lerp/Slerp.

I thought I had it but for some reason my code only works when the object is rotated 90 degrees (i.e when the up direction is the Z rather than Y).

I've been banging my head on this for a while and I really can't figure it out. I must have a misunderstanding of some of the concepts I'm trying to use. The movement seems to be fine but the rotation only works when the objects are rotated as described above (image I have a sheet of paper object which by default is stood upright with Y being the top, when the game start it falls to the ground and the Z is now facing up).

These are the two moving and rotating functions:

     void RotateTowardCam (){
         Vector3 relativePosition =  trans.position - secondaryCam.GetComponent<Transform> ().position;
         targetRotation = Quaternion.LookRotation (relativePosition, new Vector3 (0, 0, -1));
         secondaryCam.GetComponent<Transform> ().rotation = Quaternion.Slerp (secondaryCam.GetComponent<Transform> ().rotation, targetRotation, Time.deltaTime * rotateSpeed);
         //Debug.Log (trans.rotation + " " + targetRotation + " " + secondaryCam.GetComponent<Transform> ().rotation);
     }
 
     IEnumerator MoveCameraToward (Vector3 startPos)
     {
         float distCovered = 0f;
         while (trans.localPosition != secondaryCam.GetComponent<Transform> ().position * offsetFromCam && secondaryCam.GetComponent<Camera>().fieldOfView != zoomFOV) {
             distCovered += Time.deltaTime * lookAtSpeed;
             secondaryCam.GetComponent<Transform> ().position = Vector3.Lerp (startPos, trans.position + trans.forward * offsetFromCam, distCovered);
 
             secondaryCam.GetComponent<Camera> ().fieldOfView = Mathf.Lerp (secondaryCam.GetComponent<Camera> ().fieldOfView, zoomFOV, Time.deltaTime * lookAtSpeed);
             yield return new WaitForSeconds (0.0f);
         }
     }

And this is the entire class:

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class LookAtOnClick : MonoBehaviour {
 
     private Rigidbody body;
     private Collider col;
     private Transform trans;
     public GameObject playerCam;
     public GameObject secondaryCam;
     public float lookAtSpeed;
     public float rotateSpeed;
     public float offsetFromCam;
     public float zoomFOV;
 
     private Quaternion targetRotation;
     private bool currentlyLooked;
 
     private void Awake()
     {
         // Assuming a simple, flat hierarchy
         body = GetComponent<Rigidbody>();
         col = GetComponent<Collider>();
     }
 
     public void Start (){
         trans = GetComponent<Transform>();
     }
 
     void Update(){
         if (currentlyLooked) {
             RotateTowardCam ();
         }
     }
 
     public void HitByRay () {
         //Debug.Log ("I was hit by a Ray");
         LookAtItem ();
     }
 
     private void LookAtItem(){
         if (Input.GetButtonDown ("Fire1")) {
             secondaryCam.SetActive (true);
             secondaryCam.GetComponent<Transform> ().position = Camera.main.transform.position;
             secondaryCam.GetComponent<Transform> ().rotation = Camera.main.transform.rotation;
             secondaryCam.GetComponent<Camera> ().fieldOfView = Camera.main.fieldOfView;
             StartCoroutine (MoveCameraToward (secondaryCam.GetComponent<Transform> ().position));
             currentlyLooked = true;
             Camera.main.enabled = false;
             EventManager.TriggerEvent ("InViewMode");
         }
     }
 
     void RotateTowardCam (){
         Vector3 relativePosition =  trans.position - secondaryCam.GetComponent<Transform> ().position;
         targetRotation = Quaternion.LookRotation (relativePosition, new Vector3 (0, 0, -1));
         secondaryCam.GetComponent<Transform> ().rotation = Quaternion.Slerp (secondaryCam.GetComponent<Transform> ().rotation, targetRotation, Time.deltaTime * rotateSpeed);
         //Debug.Log (trans.rotation + " " + targetRotation + " " + secondaryCam.GetComponent<Transform> ().rotation);
     }
 
     IEnumerator MoveCameraToward (Vector3 startPos)
     {
         float distCovered = 0f;
         while (trans.localPosition != secondaryCam.GetComponent<Transform> ().position * offsetFromCam && secondaryCam.GetComponent<Camera>().fieldOfView != zoomFOV) {
             distCovered += Time.deltaTime * lookAtSpeed;
             secondaryCam.GetComponent<Transform> ().position = Vector3.Lerp (startPos, trans.position + trans.forward * offsetFromCam, distCovered);
 
             secondaryCam.GetComponent<Camera> ().fieldOfView = Mathf.Lerp (secondaryCam.GetComponent<Camera> ().fieldOfView, zoomFOV, Time.deltaTime * lookAtSpeed);
             yield return null;
         }
     }
 }

Thank you for your help.