diff --git a/gtsam/geometry/tests/testOrientedPlane3.cpp b/gtsam/geometry/tests/testOrientedPlane3.cpp
index c6189b970..1fd9d9d6b 100644
--- a/gtsam/geometry/tests/testOrientedPlane3.cpp
+++ b/gtsam/geometry/tests/testOrientedPlane3.cpp
@@ -30,7 +30,7 @@ GTSAM_CONCEPT_TESTABLE_INST(OrientedPlane3)
 GTSAM_CONCEPT_MANIFOLD_INST(OrientedPlane3)
 
 //*******************************************************************************
-TEST (OrientedPlane3, get) {
+TEST (OrientedPlane3, getMethods) {
   Vector4 c;
   c << -1, 0, 0, 5;
   OrientedPlane3 plane1(c);
@@ -38,11 +38,13 @@ TEST (OrientedPlane3, get) {
   Vector4 coefficient1 = plane1.planeCoefficients();
   double distance1 = plane1.distance();
   EXPECT(assert_equal(coefficient1, c, 1e-8));
+  EXPECT(assert_equal(Unit3(-1,0,0).unitVector(), plane1.normal().unitVector()));
   EXPECT_DOUBLES_EQUAL(distance1, 5, 1e-8);
   Vector4 coefficient2 = plane2.planeCoefficients();
   double distance2 = plane2.distance();
   EXPECT(assert_equal(coefficient2, c, 1e-8));
   EXPECT_DOUBLES_EQUAL(distance2, 5, 1e-8);
+  EXPECT(assert_equal(Unit3(-1,0,0).unitVector(), plane2.normal().unitVector()));
 }
 
 //*******************************************************************************
@@ -98,11 +100,11 @@ inline static Vector randomVector(const Vector& minLimits,
 TEST(OrientedPlane3, localCoordinates_retract) {
 
   size_t numIterations = 10000;
-  gtsam::Vector minPlaneLimit(4), maxPlaneLimit(4);
+  Vector4 minPlaneLimit, maxPlaneLimit;
   minPlaneLimit << -1.0, -1.0, -1.0, 0.01;
   maxPlaneLimit << 1.0, 1.0, 1.0, 10.0;
 
-  Vector minXiLimit(3), maxXiLimit(3);
+  Vector3 minXiLimit, maxXiLimit;
   minXiLimit << -M_PI, -M_PI, -10.0;
   maxXiLimit << M_PI, M_PI, 10.0;
   for (size_t i = 0; i < numIterations; i++) {
@@ -114,15 +116,15 @@ TEST(OrientedPlane3, localCoordinates_retract) {
     Vector v12 = randomVector(minXiLimit, maxXiLimit);
 
     // Magnitude of the rotation can be at most pi
-    if (v12.segment<3>(0).norm() > M_PI)
-      v12.segment<3>(0) = v12.segment<3>(0) / M_PI;
+    if (v12.head<3>().norm() > M_PI)
+      v12.head<3>() = v12.head<3>() / M_PI;
     OrientedPlane3 p2 = p1.retract(v12);
 
     // Check if the local coordinates and retract return the same results.
     Vector actual_v12 = p1.localCoordinates(p2);
-    EXPECT(assert_equal(v12, actual_v12, 1e-3));
+    EXPECT(assert_equal(v12, actual_v12, 1e-6));
     OrientedPlane3 actual_p2 = p1.retract(actual_v12);
-    EXPECT(assert_equal(p2, actual_p2, 1e-3));
+    EXPECT(assert_equal(p2, actual_p2, 1e-6));
   }
 }