diff --git a/.gitignore b/.gitignore
index eb5a316..79c6133 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1 +1,2 @@
 target
+rusty-tags.vi
diff --git a/structs/src/lib.rs b/structs/src/lib.rs
index cc9cbe1..692dd67 100644
--- a/structs/src/lib.rs
+++ b/structs/src/lib.rs
@@ -62,6 +62,39 @@ impl Tuple {
         self.w == 0.0
     }
 
+    fn magnitude(&self) -> f32 {
+        (
+            (self.x * self.x) +
+            (self.y * self.y) +
+            (self.z * self.z) +
+            (self.w * self.w)
+        ).sqrt()
+    }
+
+    fn normalize(&self) -> Tuple {
+        let m = self.magnitude();
+        Tuple::new(
+            self.x / m,
+            self.y / m,
+            self.z / m,
+            self.w / m,
+        )
+    }
+
+    fn dot(&self, rhs: &Tuple) -> f32 {
+        self.x * rhs.x +
+            self.y * rhs.y +
+            self.z * rhs.z +
+            self.w * rhs.w
+    }
+
+    fn cross(&self, rhs: &Tuple) -> Tuple {
+        Tuple::vector(
+            self.y * rhs.z - self.z * rhs.y,
+            self.z * rhs.x - self.x * rhs.z,
+            self.x * rhs.y - self.y * rhs.x
+        )
+    }
 }
 
 impl PartialEq for Tuple {
@@ -294,4 +327,84 @@ mod tests {
  
          assert_eq!(result, a / 2.0);
      }
+
+     #[test]
+     fn magnitude_x() {
+         let v = Tuple::vector(1.0, 0.0, 0.0);
+         assert_eq!(1.0, v.magnitude());
+     }
+
+     #[test]
+     fn magnitude_y() {
+         let v = Tuple::vector(0.0, 1.0, 0.0);
+         assert_eq!(1.0, v.magnitude());
+     }
+
+     #[test]
+     fn magnitude_z() {
+         let v = Tuple::vector(0.0, 0.0, 1.0);
+         assert_eq!(1.0, v.magnitude());
+     }
+
+     #[test]
+     fn magnitude_123() {
+         let v = Tuple::vector(1.0, 2.0, 3.0);
+         assert_eq!(14.0_f32.sqrt(), v.magnitude());
+     }
+
+     #[test]
+     fn magnitude_123_neg() {
+         let v = Tuple::vector(-1.0, -2.0, -3.0);
+         assert_eq!(14.0_f32.sqrt(), v.magnitude());
+     }
+
+     #[test]
+     fn normalize_x() {
+         let v = Tuple::vector(4.0, 0.0, 0.0);
+         let norm = v.normalize();
+
+         let result = Tuple::vector(1.0, 0.0, 0.0);
+         assert_eq!(result, norm);
+         
+     }
+
+     #[test]
+     fn normalize_123() {
+         let v = Tuple::vector(1.0, 2.0, 3.0);
+         let norm = v.normalize();
+
+
+         let sqrt_of_14 = 14.0_f32.sqrt();
+         assert_relative_eq!(norm.x, 1.0 / sqrt_of_14);
+         assert_relative_eq!(norm.y, 2.0 / sqrt_of_14);
+         assert_relative_eq!(norm.z, 3.0 / sqrt_of_14);
+     }
+
+     #[test]
+     fn normalize_magnitude() {
+         let v = Tuple::vector(1.0, 2.0, 3.0);
+         let norm = v.normalize();
+         let m = norm.magnitude();
+
+         assert_relative_eq!(1.0, m);
+     }
+
+     #[test]
+     fn dot_product() {
+         let a = Tuple::vector(1.0, 2.0, 3.0);
+         let b = Tuple::vector(2.0, 3.0, 4.0);
+
+         assert_eq!(20.0, a.dot(&b));
+     }
+
+     #[test]
+     fn cross_product() {
+         let a = Tuple::vector(1.0, 2.0, 3.0);
+         let b = Tuple::vector(2.0, 3.0, 4.0);
+
+         let a_cross_b = Tuple::vector(-1.0, 2.0, -1.0);
+         assert_eq!(a_cross_b, a.cross(&b));
+         let b_cross_a = Tuple::vector(1.0, -2.0, 1.0);
+         assert_eq!(b_cross_a, b.cross(&a));
+     }
 }
diff --git a/tuples/src/lib.rs b/tuples/src/lib.rs
index 74115ae..1dea01a 100644
--- a/tuples/src/lib.rs
+++ b/tuples/src/lib.rs
@@ -9,7 +9,6 @@ fn point(x: f32, y: f32, z: f32) -> PointVector {
     (x, y, z, 1.0)
 }
 
-
 fn vector(x: f32, y: f32, z: f32) -> PointVector {
     (x, y, z, 0.0)
 }
@@ -42,30 +41,15 @@ fn tuple_equals(lhs: PointVector, rhs: PointVector) -> bool {
 }
 
 fn tuple_add(lhs: PointVector, rhs: PointVector) -> PointVector {
-    (
-        lhs.0 + rhs.0,
-        lhs.1 + rhs.1,
-        lhs.2 + rhs.2,
-        lhs.3 + rhs.3
-        )
+    (lhs.0 + rhs.0, lhs.1 + rhs.1, lhs.2 + rhs.2, lhs.3 + rhs.3)
 }
 
 fn tuple_sub(lhs: PointVector, rhs: PointVector) -> PointVector {
-    (
-        lhs.0 - rhs.0,
-        lhs.1 - rhs.1,
-        lhs.2 - rhs.2,
-        lhs.3 - rhs.3
-        )
+    (lhs.0 - rhs.0, lhs.1 - rhs.1, lhs.2 - rhs.2, lhs.3 - rhs.3)
 }
 
 fn tuple_neg(lhs: PointVector) -> PointVector {
-    (
-        -lhs.0,
-        -lhs.1,
-        -lhs.2,
-        -lhs.3
-        )
+    (-lhs.0, -lhs.1, -lhs.2, -lhs.3)
 }
 
 fn tuple_mult(lhs: PointVector, scalar: f32) -> PointVector {
@@ -74,7 +58,7 @@ fn tuple_mult(lhs: PointVector, scalar: f32) -> PointVector {
         lhs.1 * scalar,
         lhs.2 * scalar,
         lhs.3 * scalar,
-        )
+    )
 }
 
 fn tuple_div(lhs: PointVector, divisor: f32) -> PointVector {
@@ -83,7 +67,40 @@ fn tuple_div(lhs: PointVector, divisor: f32) -> PointVector {
         lhs.1 / divisor,
         lhs.2 / divisor,
         lhs.3 / divisor,
-        )
+    )
+}
+
+fn magnitude(vector: PointVector) -> f32 {
+    (
+        (vector.0 * vector.0) +
+        (vector.1 * vector.1) +
+        (vector.2 * vector.2) +
+        (vector.3 * vector.3)
+        ).sqrt()
+}
+
+fn normalize(vector: PointVector) -> PointVector {
+    let m = magnitude(vector);
+    (vector.0 / m,
+     vector.1 / m,
+     vector.2 / m,
+     vector.3 / m,
+    )
+}
+
+fn dot(lhs: PointVector, rhs: PointVector) -> f32 {
+    lhs.0 * rhs.0 +
+        lhs.1 * rhs.1 +
+        lhs.2 * rhs.2 +
+        lhs.3 * rhs.3
+}
+
+fn cross(lhs: PointVector, rhs: PointVector) -> PointVector {
+    vector(
+        lhs.1 * rhs.2 - lhs.2 * rhs.1,
+        lhs.2 * rhs.0 - lhs.0 * rhs.2,
+        lhs.0 * rhs.1 - lhs.1 * rhs.0
+    )
 }
 
 #[cfg(test)]
@@ -94,10 +111,10 @@ mod tests {
     fn get_point() {
         let tuple = (4.3, -4.2, 3.1, 1.0);
 
-        assert_relative_eq!( 4.3,  tuple_x(tuple));
-        assert_relative_eq!(-4.2,  tuple_y(tuple));
-        assert_relative_eq!( 3.1,  tuple_z(tuple));
-        assert_eq!(true,  tuple_is_point(tuple));
+        assert_relative_eq!(4.3, tuple_x(tuple));
+        assert_relative_eq!(-4.2, tuple_y(tuple));
+        assert_relative_eq!(3.1, tuple_z(tuple));
+        assert_eq!(true, tuple_is_point(tuple));
         assert_eq!(false, tuple_is_vector(tuple));
     }
 
@@ -111,11 +128,11 @@ mod tests {
     fn get_vector() {
         let tuple = (4.3, -4.2, 3.1, 0.0);
 
-        assert_relative_eq!( 4.3,  tuple_x(tuple));
-        assert_relative_eq!(-4.2,  tuple_y(tuple));
-        assert_relative_eq!( 3.1,  tuple_z(tuple));
+        assert_relative_eq!(4.3, tuple_x(tuple));
+        assert_relative_eq!(-4.2, tuple_y(tuple));
+        assert_relative_eq!(3.1, tuple_z(tuple));
         assert_eq!(false, tuple_is_point(tuple));
-        assert_eq!(true,  tuple_is_vector(tuple));
+        assert_eq!(true, tuple_is_vector(tuple));
     }
 
     #[test]
@@ -221,4 +238,84 @@ mod tests {
 
         assert_eq!(true, tuple_equals(result, tuple_div(a, 2.0)));
     }
+
+    #[test]
+    fn compute_magnitude_x() {
+        let v = vector(1.0, 0.0, 0.0);
+
+        assert_eq!(1.0, magnitude(v));
+    }
+
+    #[test]
+    fn compute_magnitude_y() {
+        let v = vector(0.0, 1.0, 0.0);
+
+        assert_eq!(1.0, magnitude(v));
+    }
+
+    #[test]
+    fn compute_magnitude_z() {
+        let v = vector(0.0, 0.0, 1.0);
+
+        assert_eq!(1.0, magnitude(v));
+    }
+
+    #[test]
+    fn compute_magnitude_123() {
+        let v = vector(1.0, 2.0, 3.0);
+
+        assert_relative_eq!(14.0_f32.sqrt(), magnitude(v));
+    }
+
+    #[test]
+    fn compute_magnitude_123_neg() {
+        let v = vector(-1.0, -2.0, -3.0);
+
+        assert_relative_eq!(14.0_f32.sqrt(), magnitude(v));
+    }
+
+    #[test]
+    fn normalize_x() {
+        let v = vector(4.0, 0.0, 0.0);
+        let norm = normalize(v);
+        assert_eq!(vector(1.0, 0.0, 0.0), norm);
+    }
+
+    #[test]
+    fn normalize_123() {
+        let v = vector(1.0, 2.0, 3.0);
+        let norm = normalize(v);
+        let sqrt_of_14 = 14.0_f32.sqrt();
+        assert_relative_eq!(norm.0, 1.0 / sqrt_of_14);
+        assert_relative_eq!(norm.1, 2.0 / sqrt_of_14);
+        assert_relative_eq!(norm.2, 3.0 / sqrt_of_14);
+    }
+
+    #[test]
+    fn magnitude_of_normalized_vector() {
+        let v = vector(1.0, 2.0, 3.0);
+        let norm = normalize(v);
+        let m = magnitude(norm);
+        assert_relative_eq!(1.0, m);
+    }
+
+    #[test]
+    fn dot_product() {
+        let a = vector(1.0, 2.0, 3.0);
+        let b = vector(2.0, 3.0, 4.0);
+
+        assert_eq!(20.0, dot(a, b));
+    }
+
+    #[test]
+    fn cross_product() {
+        let a = vector(1.0, 2.0, 3.0);
+        let b = vector(2.0, 3.0, 4.0);
+
+        let a_cross_b = vector(-1.0, 2.0, -1.0);
+        assert_eq!(a_cross_b, cross(a, b));
+        let b_cross_a = vector(1.0, -2.0, 1.0);
+        assert_eq!(b_cross_a, cross(b, a));
+
+    }
 }