CosProjectionDot

using UnityEngine;

public class NewBehaviourScript : MonoBehaviour
{
    [SerializeField] private Vector2 _a;
    [SerializeField] private Vector2 _b;
    [SerializeField] private float _aAngle = 45;
    [SerializeField] private float _bAngle;
    [SerializeField] private float _aMagnitude = 1;
    [SerializeField] private float _bMagnitude = 1;

    private void Update()
    {
        _a = Vector2Extension.GetRotatedVector(Vector2.right, _aAngle * Mathf.Deg2Rad) * _aMagnitude;
        _b = Vector2Extension.GetRotatedVector(Vector2.right, _bAngle * Mathf.Deg2Rad) * _bMagnitude;

        float dot = Vector2.Dot(_a, _b);
        float cos = dot / (_b.magnitude * _a.magnitude);
        float AonBProjection = dot / (_b.magnitude);

        Debug.DrawRay(transform.position, _a, Color.cyan);
        Debug.DrawRay(transform.position, _b, Color.magenta);
        Debug.DrawRay(transform.position + Vector3.down * 0.01f, _b.normalized * cos, Color.red);
        Debug.DrawRay(transform.position + Vector3.down * 0.02f, _b.normalized * AonBProjection, Color.green);
        Debug.DrawRay(transform.position + Vector3.down * 0.03f, _b.normalized * dot, Color.blue);
        Debug.DrawLine(Vector3.down * 0.02f + (Vector3)_b.normalized * AonBProjection, (Vector3)_a, Color.yellow);
    }
}

public static class Vector2Extension
{
    public static Vector2 GetDirectionAlongCircle(Vector2 targetPositioin, Vector2 selfPoisition, float speed)
    {
        Vector2 r = selfPoisition - targetPositioin;
        float angle = GetRotationAngle(r.magnitude, speed);
        Vector2 rotatedR = GetRotatedVector(r, angle);
        return (rotatedR - r).normalized;

        float GetRotationAngle(float r, float chord) =>
            Mathf.Asin(chord / (2 * r)) * 2;
    }
    public static Vector2 GetRotatedVector(Vector2 vector, float rad)
    {
        Vector2 right = new Vector2(Mathf.Cos(rad), Mathf.Sin(rad));
        Vector2 up = new Vector2(-Mathf.Sin(rad), Mathf.Cos(rad));
        return new Vector2(right.x * vector.x + up.x * vector.y,
                           right.y * vector.x + up.y * vector.y);
    }
}