double *add_3d_vectors3(double a[3], double b[3])
{
  double *sum;
  sum = (double *)malloc(3*sizeof(double));
  if ( sum == NULL )
    return NULL;
  sum[0] = a[0] + b[0];
  sum[1] = a[1] + b[1];
  sum[2] = a[2] + b[2];
  return sum;
}