So, I previously wasn't really in the practice of writing unit tests - now I kind of am and I need to check if I'm on the right track.

Say you have a class that deals with math computations.

class Vector3
{
public:  // Yes, public.
  float x,y,z ;
  // ... ctors ...
} ;

Vector3 operator+( const Vector3& a, const Vector3 &b )
{
  return Vector3( a.x + b.y /* oops!! hence the need for unit testing.. */,
                  a.y + b.y,
                  a.z + b.z ) ;
}

There are 2 ways I can really think of to do a unit test on a Vector class:

1) Hand-solve some problems, then hard code the numbers into the unit test and pass only if equal to your hand and hard-coded result

bool UnitTest_ClassVector3_operatorPlus()
{
  Vector3 a( 2, 3, 4 ) ;
  Vector3 b( 5, 6, 7 ) ;

  Vector3 result = a + b ;

  // "expected" is computed outside of computer, and
  // hard coded here.  For more complicated operations like
  // arbitrary axis rotation this takes a bit of paperwork,
  // but only the final result will ever be entered here.
  Vector3 expected( 7, 9, 11 ) ;

  if( result.isNear( expected ) )
    return PASS ;
  else
    return FAIL ;
}

2) Rewrite the computation code very carefully inside the unit test.

bool UnitTest_ClassVector3_operatorPlus()
{
  Vector3 a( 2, 3, 4 ) ;
  Vector3 b( 5, 6, 7 ) ;

  Vector3 result = a + b ;

  // "expected" is computed HERE.  This
  // means all you've done is coded the
  // same thing twice, hopefully not having
  // repeated the same mistake again
  Vector3 expected( 2 + 5, 6 + 3, 4 + 7 ) ;

  if( result.isNear( expected ) )
    return PASS ;
  else
    return FAIL ;
}

Or is there another way to do something like this?