diff --git a/.github/workflows/array-api-skips.txt b/.github/workflows/array-api-skips.txt
index bfbf71e906d4..097e6ffef42b 100644
--- a/.github/workflows/array-api-skips.txt
+++ b/.github/workflows/array-api-skips.txt
@@ -34,9 +34,5 @@ array_api_tests/test_operators_and_elementwise_functions.py::test_asinh
 array_api_tests/test_signatures.py::test_func_signature[std]
 array_api_tests/test_signatures.py::test_func_signature[var]
 
-# wrong shape is returned
-array_api_tests/test_linalg.py::test_vecdot
-array_api_tests/test_linalg.py::test_linalg_vecdot
-
 # arrays have different values
 array_api_tests/test_linalg.py::test_linalg_tensordot
diff --git a/dpnp/dpnp_utils/dpnp_utils_linearalgebra.py b/dpnp/dpnp_utils/dpnp_utils_linearalgebra.py
index 7752da531a25..f90c95370cd4 100644
--- a/dpnp/dpnp_utils/dpnp_utils_linearalgebra.py
+++ b/dpnp/dpnp_utils/dpnp_utils_linearalgebra.py
@@ -198,13 +198,14 @@ def _define_dim_flags(x, axis):
     """
     Define useful flags for the calculations in dpnp_matmul and dpnp_vecdot.
     x_is_1D: `x` is 1D array or inherently 1D (all dimensions are equal to one
-    except for one of them), for instance, if x.shape = (1, 1, 1, 2),
-    then x_is_1D = True
+    except for dimension at `axis`), for instance, if x.shape = (1, 1, 1, 2),
+    and axis=-1, then x_is_1D = True.
     x_is_2D: `x` is 2D array or inherently 2D (all dimensions are equal to one
     except for the last two of them), for instance, if x.shape = (1, 1, 3, 2),
-    then x_is_2D = True
+    then x_is_2D = True.
     x_base_is_1D: `x` is 1D considering only its last two dimensions, for instance,
-    if x.shape = (3, 4, 1, 2), then x_base_is_1D = True
+    if x.shape = (3, 4, 1, 2), then x_base_is_1D = True.
+
     """
 
     x_shape = x.shape
@@ -326,14 +327,11 @@ def _get_result_shape_vecdot(x1, x2, x1_ndim, x2_ndim):
     if x1_shape[-1] != x2_shape[-1]:
         _shape_error(x1_shape[-1], x2_shape[-1], "vecdot", err_msg=0)
 
-    _, x1_is_1D, _ = _define_dim_flags(x1, axis=-1)
-    _, x2_is_1D, _ = _define_dim_flags(x2, axis=-1)
-
     if x1_ndim == 1 and x2_ndim == 1:
         result_shape = ()
-    elif x1_is_1D:
+    elif x1_ndim == 1:
         result_shape = x2_shape[:-1]
-    elif x2_is_1D:
+    elif x2_ndim == 1:
         result_shape = x1_shape[:-1]
     else:  # at least 2D
         if x1_ndim != x2_ndim:
diff --git a/dpnp/tests/test_product.py b/dpnp/tests/test_product.py
index eab4fe9f53ec..09dfa7d815f2 100644
--- a/dpnp/tests/test_product.py
+++ b/dpnp/tests/test_product.py
@@ -1000,6 +1000,8 @@ def setup_method(self):
             ((1, 4, 5), (3, 1, 5)),
             ((1, 1, 4, 5), (3, 1, 5)),
             ((1, 4, 5), (1, 3, 1, 5)),
+            ((2, 1), (1, 1, 1)),
+            ((1, 1, 3), (3,)),
         ],
     )
     def test_basic(self, dtype, shape1, shape2):