diff --git a/rtchallenge/src/tuples.rs b/rtchallenge/src/tuples.rs
index 2ad9788..ce091ad 100644
--- a/rtchallenge/src/tuples.rs
+++ b/rtchallenge/src/tuples.rs
@@ -113,11 +113,22 @@ fn tuple(x: f32, y: f32, z: f32, w: f32) -> Tuple {
     Tuple { x, y, z, w }
 }
 
+fn dot(a: Tuple, b: Tuple) -> f32 {
+    a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w
+}
+fn cross(a: Tuple, b: Tuple) -> Tuple {
+    vector(
+        a.y * b.z - a.z * b.y,
+        a.z * b.x - a.x * b.z,
+        a.x * b.y - a.y * b.x,
+    )
+}
+
 #[cfg(test)]
 mod tests {
     use float_cmp::approx_eq;
 
-    use super::{point, tuple, vector};
+    use super::{cross, dot, point, tuple, vector};
     #[test]
     fn is_point() {
         // A tuple with w = 1 is a point
@@ -225,4 +236,17 @@ mod tests {
             ulps = 1
         ));
     }
+    #[test]
+    fn dot_two_tuples() {
+        let a = vector(1., 2., 3.);
+        let b = vector(2., 3., 4.);
+        assert_eq!(20., dot(a, b));
+    }
+    #[test]
+    fn cross_two_tuples() {
+        let a = vector(1., 2., 3.);
+        let b = vector(2., 3., 4.);
+        assert_eq!(vector(-1., 2., -1.), cross(a, b));
+        assert_eq!(vector(1., -2., 1.), cross(b, a));
+    }
 }