diff --git a/src/array_api_stubs/_draft/linalg.py b/src/array_api_stubs/_draft/linalg.py
index d05b53a9f..1e7efa95e 100644
--- a/src/array_api_stubs/_draft/linalg.py
+++ b/src/array_api_stubs/_draft/linalg.py
@@ -83,15 +83,15 @@ def cross(x1: array, x2: array, /, *, axis: int = -1) -> array:
     Parameters
     ----------
     x1: array
-        first input array. Must have a numeric data type.
+        first input array. Must have a numeric data type. The size of the axis over which the cross product is to be computed must be equal to 3.
     x2: array
-        second input array. Must be compatible with ``x1`` for all non-compute axes (see :ref:`broadcasting`). The size of the axis over which to compute the cross product must be the same size as the respective axis in ``x1``. Must have a numeric data type.
+        second input array. Must be broadcast compatible with ``x1`` along all axes other than the axis along which the cross-product is computed (see :ref:`broadcasting`). The size of the axis over which the cross product is to be computed must be equal to 3. Must have a numeric data type.
 
         .. note::
            The compute axis (dimension) must not be broadcasted.
 
     axis: int
-        the axis (dimension) of ``x1`` and ``x2`` containing the vectors for which to compute the cross product. Must be an integer on the interval ``[-N, N)``, where ``N`` is the rank (number of dimensions) of the shape determined according to :ref:`broadcasting`. If specified as a negative integer, the function must determine the axis along which to compute the cross product by counting backward from the last dimension (where ``-1`` refers to the last dimension). By default, the function must compute the cross product over the last axis. Default: ``-1``.
+        the axis (dimension) of ``x1`` and ``x2`` containing the vectors for which to compute the cross product. Should be an integer on the interval ``[-N, -1]``, where ``N`` is ``min(x1.ndim, x2.ndim)``. The function must determine the axis along which to compute the cross product by counting backward from the last dimension (where ``-1`` refers to the last dimension). By default, the function must compute the cross product over the last axis. Default: ``-1``.
 
     Returns
     -------
@@ -110,8 +110,7 @@ def cross(x1: array, x2: array, /, *, axis: int = -1) -> array:
 
     **Raises**
 
-    -   if the size of the axis over which to compute the cross product is not equal to ``3``.
-    -   if the size of the axis over which to compute the cross product is not the same (before broadcasting) for both ``x1`` and ``x2``.
+    -   if the size of the axis over which to compute the cross product is not equal to ``3`` (before broadcasting) for both ``x1`` and ``x2``.
     """
 
 
diff --git a/src/array_api_stubs/_draft/linear_algebra_functions.py b/src/array_api_stubs/_draft/linear_algebra_functions.py
index 96f082bd5..eea898a6b 100644
--- a/src/array_api_stubs/_draft/linear_algebra_functions.py
+++ b/src/array_api_stubs/_draft/linear_algebra_functions.py
@@ -141,7 +141,7 @@ def vecdot(x1: array, x2: array, /, *, axis: int = -1) -> array:
            The contracted axis (dimension) must not be broadcasted.
 
     axis: int
-        axis over which to compute the dot product. Must be an integer on the interval ``[-N, N)``, where ``N`` is the rank (number of dimensions) of the shape determined according to :ref:`broadcasting`. If specified as a negative integer, the function must determine the axis along which to compute the dot product by counting backward from the last dimension (where ``-1`` refers to the last dimension). By default, the function must compute the dot product over the last axis. Default: ``-1``.
+        the axis (dimension) of ``x1`` and ``x2`` containing the vectors for which to compute the dot product. Should be an integer on the interval ``[-N, -1]``, where ``N`` is ``min(x1.ndim, x2.ndim)``. The function must determine the axis along which to compute the dot product by counting backward from the last dimension (where ``-1`` refers to the last dimension). By default, the function must compute the dot product over the last axis. Default: ``-1``.
 
     Returns
     -------