diff --git a/src/hello_world/__init__.py b/src/hello_world/__init__.py
index ec0a87d..5ecf5d9 100644
--- a/src/hello_world/__init__.py
+++ b/src/hello_world/__init__.py
@@ -1,12 +1,51 @@
 import math
+from typing import NamedTuple
 
+class  Vector(NamedTuple):
+    x: float
+    y: float
+
+current_pos = Vector(3,2)
+target_pos = Vector(7,5)
+zero_vector = Vector(0,0)
 
 def main() -> None:
-    print("Hello from hello-world!")
-    print(lenght(3,4))
+    print("Hello Teodora!")
 
-def lenght(x,y):
-    squared_x = x*x
-    squared_y = y*y
+    distance = displacementVector(current_pos, target_pos)
+    print(distance)
+
+    lengthOfDistanceVector =  length(distance)
+    print(lengthOfDistanceVector)
+
+    direction = safe_normalize(distance, 0.001)
+    print(direction)
+
+## calculate the displacement from current position to target position
+
+
+def displacementVector(current_pos, target_pos):
+    displacementVector = Vector(target_pos.x - current_pos.x, target_pos.y - current_pos.y)
+    return displacementVector
+
+## distance between two positions
+# Euclidian norm
+
+def length(vector: Vector) -> float:
+    squared_x = vector.x*vector.x
+    squared_y = vector.y*vector.y
     squared_x + squared_y
     return math.sqrt(squared_x + squared_y)
+
+# safe normalisation
+# The minimum-distance check also prevents division by zero.
+
+def safe_normalize(vector: Vector, minimum_distance: float) -> Vector:
+    vector_length = length(vector)
+
+    if vector_length < minimum_distance:
+     return zero_vector
+
+    einheitsVector = Vector(vector.x / vector_length, vector.y / vector_length)
+    return einheitsVector
+