@Hanna the flag belongs over the diagram. But the arrows are right. Thanks.

I finished the solution and I wanted to post the code:

%matplotlib inline
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from ipywidgets import interact, Output
from IPython.display import display

# Beispiel-Daten erstellen
data = {
    'Club Path': [5.89, 5.2, 4.9, 5.7],
    'Face Angle': [3.12, 2.8, 3.3, 2.7]
}
df = pd.DataFrame(data)

# Ausgabe-Widget für das Diagramm
output = Output()

# Interaktive Tabelle erstellen
def create_table():
    table = pd.DataFrame(df)
    display(table)

# Funktion zum Zeichnen des Diagramms
def plot_data(selected_row):
    # Calculating the angle in radians
    selected_data = df.iloc[selected_row]
    club_path = np.radians(selected_data['Club Path'])  # Club Path
    face_angle = np.radians(selected_data['Face Angle'])  # Face Angle

    # Create a figure and an axis
    fig, ax = plt.subplots()

    # Axis limits
    ax.set_xlim(-1, 1)
    ax.set_ylim(-1, 1)

    # Draw x- and y-axis
    ax.axhline(0, color='black', linewidth=0.5, ls='--')
    ax.axvline(0, color='black', linewidth=1.5, ls='--')

    # Draw angles
    club_vector = np.array([np.sin(club_path), np.cos(club_path)])
    face_vector = np.array([np.sin(face_angle), np.cos(face_angle)])

    ax.quiver(0, 0, club_vector[0], club_vector[1], angles='xy', scale_units='xy', scale=1, color='blue', label='Club Path (5.89°)')
    ax.quiver(0, 0, face_vector[0], face_vector[1], angles='xy', scale_units='xy', scale=1, color='orange', label='Face Angle (3.12°)')

    # draw lines
    ax.plot([0, -club_vector[0]], [0, -club_vector[1]], color='blue', linewidth=3)
    ax.plot([0, -face_vector[0]], [0, -face_vector[1]], color='orange', linewidth=3)

    # Calculte angle between the to vectors
    dot_product = np.dot(club_vector, face_vector)
    norm_club = np.linalg.norm(club_vector)
    norm_face = np.linalg.norm(face_vector)

    # Calculating the angle in radians
    angle_radians = np.arccos(dot_product / (norm_club * norm_face))
    angle_degrees = np.degrees(angle_radians)

    # Add angle in ledgend
    ax.legend(title=f"Face to Path: {angle_degrees:.2f}°")

    # Delete diagram frame
    for spine in ax.spines.values():
        spine.set_visible(False)

    # Delete x- and y-axis
    ax.set_xticks([])
    ax.set_yticks([])

    # Print diagram
    plt.show()

# Interaktive Auswahl der Zeile
def on_row_click(selected_row):
    plot_data(selected_row)

# Tabelle anzeigen
create_table()

# Interaktive Auswahl der Zeile
interact(on_row_click, selected_row=(0, len(df)-1))

# Ausgabe-Widget anzeigen
display(output)

This is the solution. The only downside you need to klick the selector instead of the table row you wanna show.