diff --git a/src/basics/vector.cc b/src/basics/vector.cc
index d9c2c73..ded5a3e 100644
--- a/src/basics/vector.cc
+++ b/src/basics/vector.cc
@@ -3,6 +3,8 @@
  * Eryn Wells <eryn@erynwells.me>
  */
 
+#include <cmath>
+
 #include "basics/vector.hh"
 
 
@@ -60,6 +62,50 @@ Vector4::Z()
     return mData[2];
 }
 
+
+/*
+ * charles::basics::Vector4::length2 --
+ */
+Double
+Vector4::Length2()
+    const
+{
+    return mData[0] * mData[0] + mData[1] * mData[1] + mData[2] * mData[2];
+}
+
+
+Double
+Vector4::Length()
+    const
+{
+    return std::sqrt(Length2());
+}
+
+
+Double
+Vector4::Dot(const Vector4& rhs)
+    const
+{
+    return mData[0] * rhs.mData[0] + mData[1] * rhs.mData[1] + mData[2] + rhs.mData[2];
+}
+
+
+Vector4
+Vector4::Cross(const Vector4& rhs)
+    const
+{
+    return Vector4(mData[1]*rhs.mData[2] - mData[2]*rhs.mData[1],
+                   mData[2]*rhs.mData[0] - mData[0]*rhs.mData[2],
+                   mData[0]*rhs.mData[1] - mData[1]*rhs.mData[0]);
+}
+
+
+Vector4&
+Vector4::Normalize()
+{
+    return *this /= Length();
+}
+
 } /* namespace basics */
 } /* namespace charles */
 
diff --git a/src/basics/vector.hh b/src/basics/vector.hh
index 3c8f8ff..2ef9df4 100644
--- a/src/basics/vector.hh
+++ b/src/basics/vector.hh
@@ -28,8 +28,27 @@ struct Vector4
     Double& X();
     Double& Y();
     Double& Z();
+
+    /** Get the length-squared of this vector. */
+    Double Length2() const;
+
+    /** Get the length of this vector. */
+    Double Length() const;
+
+    /** Get the dot product of `this` and `rhs`. */
+    Double Dot(const Vector4& rhs) const;
+
+    /** Get the cross product of `this` and `rhs`. */
+    Vector4 Cross(const Vector4& rhs) const;
+
+    /** Normalize this vector. */
+    Vector4& Normalize();
 };
 
+
+/** Normalize the given vector and return a copy of it. */
+Vector4& Normalized(const Vector4& v);
+
 } /* namespace basics */
 } /* namespace charles */