diff --git a/orix/quaternion/quaternion.py b/orix/quaternion/quaternion.py
index e7fdf5e2..28f355f3 100644
--- a/orix/quaternion/quaternion.py
+++ b/orix/quaternion/quaternion.py
@@ -240,7 +240,8 @@ def __mul__(self, other: Union[Quaternion, Vector3d]):
                 m.coordinate_format = other.coordinate_format
                 return m
             else:
-                return other.__class__(v)
+                kwargs = other.get_kwargs(v, rotation=self)
+                return other.__class__(**kwargs)
         return NotImplemented
 
     def __neg__(self) -> Quaternion:
diff --git a/orix/vector/miller.py b/orix/vector/miller.py
index f8a573f8..bd9e5f8f 100644
--- a/orix/vector/miller.py
+++ b/orix/vector/miller.py
@@ -161,6 +161,10 @@ def hkl(self) -> np.ndarray:
         """
         return _transform_space(self.data, "c", "r", self.phase.structure.lattice)
 
+    def get_kwargs(self, new_data, *args, **kwargs) -> dict:
+        """Return the keyword arguments to create the instance."""
+        return dict(xyz=new_data)
+
     @hkl.setter
     def hkl(self, value: np.ndarray):
         """Set the reciprocal lattice vectors."""
diff --git a/orix/vector/vector3d.py b/orix/vector/vector3d.py
index a565ba71..e1bc04be 100644
--- a/orix/vector/vector3d.py
+++ b/orix/vector/vector3d.py
@@ -219,31 +219,36 @@ def polar(self) -> np.ndarray:
     # ------------------------ Dunder methods ------------------------ #
 
     def __neg__(self) -> Vector3d:
-        return self.__class__(-self.data)
+        kwargs = self.get_kwargs(new_data=-self.data)
+        return self.__class__(**kwargs)
 
     def __add__(
         self, other: Union[int, float, List, Tuple, np.ndarray, Vector3d]
     ) -> Vector3d:
         if isinstance(other, Vector3d):
-            return self.__class__(self.data + other.data)
+            kwargs = self.get_kwargs(new_data=self.data + other.data)
+            return self.__class__(**kwargs)
         elif isinstance(other, (int, float)):
-            return self.__class__(self.data + other)
+            kwargs = self.get_kwargs(new_data=self.data + other)
+            return self.__class__(**kwargs)
         elif isinstance(other, (list, tuple)):
             other = np.array(other)
-
         if isinstance(other, np.ndarray):
-            return self.__class__(self.data + other[..., np.newaxis])
+            kwargs = self.get_kwargs(new_data=self.data + other[..., np.newaxis])
+            return self.__class__(**kwargs)
 
         return NotImplemented
 
     def __radd__(self, other: Union[int, float, List, Tuple, np.ndarray]) -> Vector3d:
         if isinstance(other, (int, float)):
-            return self.__class__(other + self.data)
+            kwargs = self.get_kwargs(new_data=other + self.data)
+            return self.__class__(**kwargs)
         elif isinstance(other, (list, tuple)):
             other = np.array(other)
 
         if isinstance(other, np.ndarray):
-            return self.__class__(other[..., np.newaxis] + self.data)
+            kwargs = self.get_kwargs(new_data=other[..., np.newaxis] + self.data)
+            return self.__class__(**kwargs)
 
         return NotImplemented
 
@@ -251,14 +256,17 @@ def __sub__(
         self, other: Union[int, float, List, Tuple, np.ndarray, Vector3d]
     ) -> Vector3d:
         if isinstance(other, Vector3d):
-            return self.__class__(self.data - other.data)
+            kwargs = self.get_kwargs(new_data=self.data - other.data)
+            return self.__class__(**kwargs)
         elif isinstance(other, (int, float)):
-            return self.__class__(self.data - other)
+            kwargs = self.get_kwargs(self.data - other)
+            return self.__class__(**kwargs)
         elif isinstance(other, (list, tuple)):
             other = np.array(other)
 
         if isinstance(other, np.ndarray):
-            return self.__class__(self.data - other[..., np.newaxis])
+            kwargs = self.get_kwargs(self.data - other[..., np.newaxis])
+            return self.__class__(**kwargs)
 
         return NotImplemented
 
@@ -282,23 +290,27 @@ def __mul__(
                 "Try `.dot` or `.cross` instead."
             )
         elif isinstance(other, (int, float)):
-            return self.__class__(self.data * other)
+            kwargs = self.get_kwargs(new_data=self.data * other)
+            return self.__class__(**kwargs)
         elif isinstance(other, (list, tuple)):
             other = np.array(other)
 
         if isinstance(other, np.ndarray):
-            return self.__class__(self.data * other[..., np.newaxis])
+            kwargs = self.get_kwargs(new_data=self.data * other[..., np.newaxis])
+            return self.__class__(**kwargs)
 
         return NotImplemented
 
     def __rmul__(self, other: Union[int, float, List, Tuple, np.ndarray]) -> Vector3d:
         if isinstance(other, (int, float)):
-            return self.__class__(other * self.data)
+            kwargs = self.get_kwargs(new_data=other * self.data)
+            return self.__class__(**kwargs)
         elif isinstance(other, (list, tuple)):
             other = np.array(other)
 
         if isinstance(other, np.ndarray):
-            return self.__class__(other[..., np.newaxis] * self.data)
+            kwargs = self.get_kwargs(new_data=other[..., np.newaxis] * self.data)
+            return self.__class__(**kwargs)
 
         return NotImplemented
 
@@ -308,12 +320,14 @@ def __truediv__(
         if isinstance(other, Vector3d):
             raise ValueError("Dividing vectors is undefined")
         elif isinstance(other, (int, float)):
-            return self.__class__(self.data / other)
+            kwargs = self.get_kwargs(new_data=self.data / other)
+            return self.__class__(**kwargs)
         elif isinstance(other, (list, tuple)):
             other = np.array(other)
 
         if isinstance(other, np.ndarray):
-            return self.__class__(self.data / other[..., np.newaxis])
+            kwargs = self.get_kwargs(new_data=self.data / other[..., np.newaxis])
+            return self.__class__(**kwargs)
 
         return NotImplemented
 
@@ -731,6 +745,11 @@ def to_polar(
             polar = np.rad2deg(polar)
         return azimuth, polar, self.radial
 
+    def get_kwargs(self, new_data, *args, **kwargs) -> Dict[str, Any]:
+        """Return the dictionary of attributes to be used in the
+        constructor when applying an ufunc."""
+        return dict(data=new_data)
+
     def in_fundamental_sector(self, symmetry: "Symmetry") -> Vector3d:
         """Project vectors to a symmetry's fundamental sector (inverse
         pole figure).