Why does transform.forward when equal to 0 when multiplied not equal to 0?

Question

Im making movement for my camera in unity. The starting position for my camera is 0,0,0. When i press the W key the code i take the current position and multiply it by a movement speed and equal it to another vector 3 to then update the postion of the position of the camera. It works great but i cant understand why when i think about.

If my camera is initialised at 0,0,0 then why does transform.forward * movementSpeed not always eqaul 0? This is the same for all directions i just used W as an example

Any help would be greatly appreciated as im new to unity. Thanks

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class CameraMovement : MonoBehaviour
{
    private Vector3 newPosition;
    [SerializeField] private float movementSpeed;
    [SerializeField] private float movementTime;
    // Start is called before the first frame update
    void Start()
    {
        newPosition = transform.position; 

        Debug.Log(transform.position); //prints 0.0,0.0,0.0
        Debug.Log(transform.forward * movementSpeed); //prints 0.0,0.0,0.3
    }

    // Update is called once per frame
    void Update()
    {
        handleKeyboardInput();
    }

    void handleKeyboardInput()
    {
        if (Input.GetKey(KeyCode.W))
        {
            newPosition += (transform.forward * movementSpeed);
        }

        if (Input.GetKey(KeyCode.A))
        {
            newPosition += (transform.right * -movementSpeed);
        }

        if (Input.GetKey(KeyCode.S))
        {
            newPosition += (transform.forward * -movementSpeed);
        }

        if (Input.GetKey(KeyCode.D))
        {
            newPosition += (transform.right * movementSpeed);
        }
        
        transform.position = Vector3.Lerp(transform.position, newPosition, Time.deltaTime * movementTime);

    }
}

Answer 1

The reason your code works is becuase transform.forward and transform.right refer to the forward and right directions of you player. When you add transform.forward * speed to your newPosition, you are adding the forward direction of the player but with a magnitude (length) of your speed.

If you want to try to understand it better, you can use print(transform.forward) or print(transform.forward * speed) or do Debug.drawRay(transform.position, transform.forward)