diff --git a/impeller/geometry/geometry_unittests.cc b/impeller/geometry/geometry_unittests.cc
index 84eec3be14703..76f34073fdf9a 100644
--- a/impeller/geometry/geometry_unittests.cc
+++ b/impeller/geometry/geometry_unittests.cc
@@ -302,6 +302,53 @@ TEST(GeometryTest, MatrixMakePerspective) {
   }
 }
 
+TEST(GeometryTest, MatrixGetBasisVectors) {
+  {
+    auto m = Matrix();
+    Vector3 x = m.GetBasisX();
+    Vector3 y = m.GetBasisY();
+    Vector3 z = m.GetBasisZ();
+    ASSERT_VECTOR3_NEAR(x, Vector3(1, 0, 0));
+    ASSERT_VECTOR3_NEAR(y, Vector3(0, 1, 0));
+    ASSERT_VECTOR3_NEAR(z, Vector3(0, 0, 1));
+  }
+
+  {
+    auto m = Matrix::MakeRotationZ(Radians{kPiOver2}) *
+             Matrix::MakeRotationX(Radians{kPiOver2}) *
+             Matrix::MakeScale(Vector3(2, 3, 4));
+    Vector3 x = m.GetBasisX();
+    Vector3 y = m.GetBasisY();
+    Vector3 z = m.GetBasisZ();
+    ASSERT_VECTOR3_NEAR(x, Vector3(0, 2, 0));
+    ASSERT_VECTOR3_NEAR(y, Vector3(0, 0, 3));
+    ASSERT_VECTOR3_NEAR(z, Vector3(4, 0, 0));
+  }
+}
+
+TEST(GeometryTest, MatrixGetDirectionScale) {
+  {
+    auto m = Matrix();
+    Scalar result = m.GetDirectionScale(Vector3{1, 0, 0});
+    ASSERT_FLOAT_EQ(result, 1);
+  }
+
+  {
+    auto m = Matrix::MakeRotationX(Degrees{10}) *
+             Matrix::MakeRotationY(Degrees{83}) *
+             Matrix::MakeRotationZ(Degrees{172});
+    Scalar result = m.GetDirectionScale(Vector3{0, 1, 0});
+    ASSERT_FLOAT_EQ(result, 1);
+  }
+
+  {
+    auto m = Matrix::MakeRotationZ(Radians{kPiOver2}) *
+             Matrix::MakeScale(Vector3(3, 4, 5));
+    Scalar result = m.GetDirectionScale(Vector3{2, 0, 0});
+    ASSERT_FLOAT_EQ(result, 8);
+  }
+}
+
 TEST(GeometryTest, QuaternionLerp) {
   auto q1 = Quaternion{{0.0, 0.0, 1.0}, 0.0};
   auto q2 = Quaternion{{0.0, 0.0, 1.0}, kPiOver4};
diff --git a/impeller/geometry/matrix.h b/impeller/geometry/matrix.h
index a3c300dda1830..8bdb250b61b56 100644
--- a/impeller/geometry/matrix.h
+++ b/impeller/geometry/matrix.h
@@ -236,10 +236,20 @@ struct Matrix {
 
   Scalar GetMaxBasisLength() const;
 
+  constexpr Vector3 GetBasisX() const { return Vector3(m[0], m[1], m[2]); }
+
+  constexpr Vector3 GetBasisY() const { return Vector3(m[4], m[5], m[6]); }
+
+  constexpr Vector3 GetBasisZ() const { return Vector3(m[8], m[9], m[10]); }
+
   constexpr Vector3 GetScale() const {
-    return Vector3(Vector3(m[0], m[1], m[2]).Length(),
-                   Vector3(m[4], m[5], m[6]).Length(),
-                   Vector3(m[8], m[9], m[10]).Length());
+    return Vector3(GetBasisX().Length(), GetBasisY().Length(),
+                   GetBasisZ().Length());
+  }
+
+  constexpr Scalar GetDirectionScale(Vector3 direction) const {
+    return 1.0 / (this->Invert() * direction.Normalize()).Length() *
+           direction.Length();
   }
 
   constexpr bool IsAffine() const {
diff --git a/impeller/geometry/vector.h b/impeller/geometry/vector.h
index ad59f91d89edc..b1621f0147a1b 100644
--- a/impeller/geometry/vector.h
+++ b/impeller/geometry/vector.h
@@ -41,7 +41,7 @@ struct Vector3 {
    *
    *  @return the calculated length.
    */
-  Scalar Length() const { return sqrt(x * x + y * y + z * z); }
+  constexpr Scalar Length() const { return sqrt(x * x + y * y + z * z); }
 
   constexpr Vector3 Normalize() const {
     const auto len = Length();
@@ -130,6 +130,18 @@ struct Vector3 {
   std::string ToString() const;
 };
 
+// RHS algebraic operations with arithmetic types.
+
+template <class U, class = std::enable_if_t<std::is_arithmetic_v<U>>>
+constexpr Vector3 operator*(U s, const Vector3& p) {
+  return p * s;
+}
+
+template <class U, class = std::enable_if_t<std::is_arithmetic_v<U>>>
+constexpr Vector3 operator/(U s, const Vector3& p) {
+  return {static_cast<Scalar>(s) / p.x, static_cast<Scalar>(s) / p.y};
+}
+
 struct Vector4 {
   union {
     struct {