diff --git a/src/05/ray.ts b/src/05/ray.ts
index ff38d30..3bebd27 100644
--- a/src/05/ray.ts
+++ b/src/05/ray.ts
@@ -33,6 +33,13 @@ export default class Ray {
         // TODO: on the image plane. In addition to the coordinates (x, y), you will need the
         // TODO: width and height of the camera (i.e. the width and height of the camera's
         // TODO: image plane), and the angle alpha specifying the camera's field of view.
-        return null;
+        var temp = new Vector(0,0,0,0);
+        temp.x = x - ((camera.width-1) / 2);
+        temp.y = ((camera.height-1) / 2) - y;
+        temp.z = - ((camera.width/2) / (Math.tan(camera.alpha/2)));
+
+        temp = temp.normalize();
+
+        return new Ray(camera.origin, temp);
     }
 }
diff --git a/src/05/sphere.ts b/src/05/sphere.ts
index bbf22cc..2024b7a 100644
--- a/src/05/sphere.ts
+++ b/src/05/sphere.ts
@@ -44,6 +44,24 @@ export default class Sphere {
         // TODO: Return an Intersection or null if there was no hit. In case
         // TODO: of two hits, return the one closer to the start point of
         // TODO: the ray.
-        return null;
+
+        let c = Math.pow(ray.origin.dot(ray.direction),2) - ray.origin.dot(ray.origin) + Math.pow(this.radius,2);
+        // hier oben noch nicht berechenenm da c negativ sein kann und dann wurzel nicht funktioniert
+        
+        if(c < 0) {
+            return null;
+        } else if(c == 0) {
+            return new Intersection(t1, ); //schnittpunkt ist origin + direction * t
+
+        } else {
+            let t1 = - ray.origin.dot(ray.direction) + Math.sqrt( Math.pow(ray.origin.dot(ray.direction),2) - ray.origin.dot(ray.origin) + Math.pow(this.radius,2));
+            let t2 = - ray.origin.dot(ray.direction) - Math.sqrt( Math.pow(ray.origin.dot(ray.direction),2) - ray.origin.dot(ray.origin) + Math.pow(this.radius,2));
+
+            if(t1 < t2) {
+            return null;
+            } else {
+            return null;
+            }
+        }
     }
 }
diff --git a/src/05/vector.ts b/src/05/vector.ts
index 50ff1ad..4d20310 100644
--- a/src/05/vector.ts
+++ b/src/05/vector.ts
@@ -238,7 +238,10 @@ export default class Vector {
      */
     normalize(): Vector {
         // TODO: Normalize this vector and return it
-        return this.div(Math.sqrt(Math.pow(this.data[0],2)+Math.pow(this.data[1],2)+Math.pow(this.data[2],2)));
+        this.x = this.x/Math.sqrt(Math.pow(this.data[0],2)+Math.pow(this.data[1],2)+Math.pow(this.data[2],2));
+        this.y = this.y/Math.sqrt(Math.pow(this.data[0],2)+Math.pow(this.data[1],2)+Math.pow(this.data[2],2));
+        this.z = this.z/Math.sqrt(Math.pow(this.data[0],2)+Math.pow(this.data[1],2)+Math.pow(this.data[2],2));
+        return this;
     }
 
     /**