diff --git a/rtchallenge/Cargo.lock b/rtchallenge/Cargo.lock
index 1ed1b63..c47050a 100644
--- a/rtchallenge/Cargo.lock
+++ b/rtchallenge/Cargo.lock
@@ -1,5 +1,32 @@
 # This file is automatically @generated by Cargo.
 # It is not intended for manual editing.
+[[package]]
+name = "autocfg"
+version = "1.0.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "cdb031dd78e28731d87d56cc8ffef4a8f36ca26c38fe2de700543e627f8a464a"
+
+[[package]]
+name = "float-cmp"
+version = "0.8.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e1267f4ac4f343772758f7b1bdcbe767c218bbab93bb432acbf5162bbf85a6c4"
+dependencies = [
+ "num-traits",
+]
+
+[[package]]
+name = "num-traits"
+version = "0.2.14"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "9a64b1ec5cda2586e284722486d802acf1f7dbdc623e2bfc57e65ca1cd099290"
+dependencies = [
+ "autocfg",
+]
+
 [[package]]
 name = "rtchallenge"
 version = "0.1.0"
+dependencies = [
+ "float-cmp",
+]
diff --git a/rtchallenge/Cargo.toml b/rtchallenge/Cargo.toml
index e040b18..5fb80a0 100644
--- a/rtchallenge/Cargo.toml
+++ b/rtchallenge/Cargo.toml
@@ -7,3 +7,4 @@ edition = "2018"
 # See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
 
 [dependencies]
+float-cmp = "0.8.0"
diff --git a/rtchallenge/src/tuples.rs b/rtchallenge/src/tuples.rs
index 2a68103..2ad9788 100644
--- a/rtchallenge/src/tuples.rs
+++ b/rtchallenge/src/tuples.rs
@@ -15,6 +15,19 @@ impl Tuple {
     fn is_vector(&self) -> bool {
         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 {
+            x: self.x / m,
+            y: self.y / m,
+            z: self.z / m,
+            w: self.w / m,
+        }
+    }
 }
 
 impl Add for Tuple {
@@ -102,6 +115,8 @@ fn tuple(x: f32, y: f32, z: f32, w: f32) -> Tuple {
 
 #[cfg(test)]
 mod tests {
+    use float_cmp::approx_eq;
+
     use super::{point, tuple, vector};
     #[test]
     fn is_point() {
@@ -185,4 +200,29 @@ mod tests {
         let a = tuple(1., -2., 3., -4.);
         assert_eq!(a / 2., tuple(0.5, -1., 1.5, -2.));
     }
+    #[test]
+    fn vector_magnitude() {
+        assert_eq!(1., vector(1., 0., 0.).magnitude());
+        assert_eq!(1., vector(0., 1., 0.).magnitude());
+        assert_eq!(1., vector(0., 0., 1.).magnitude());
+        assert_eq!(14_f32.sqrt(), vector(1., 2., 3.).magnitude());
+        assert_eq!(14_f32.sqrt(), vector(-1., -2., -3.).magnitude());
+    }
+    #[test]
+    fn vector_normalize() {
+        assert_eq!(vector(1., 0., 0.), vector(4., 0., 0.).normalize());
+        assert_eq!(
+            vector(1. / 14_f32.sqrt(), 2. / 14_f32.sqrt(), 3. / 14_f32.sqrt()),
+            vector(1., 2., 3.).normalize()
+        );
+    }
+    #[test]
+    fn vector_normalize_magnitude() {
+        assert!(approx_eq!(
+            f32,
+            1.,
+            vector(1., 2., 3.).normalize().magnitude(),
+            ulps = 1
+        ));
+    }
 }