__SCREAMING_SNAKE_CASE						:   List[Any]         =			tuple[float, float, float]
__SCREAMING_SNAKE_CASE						:   str         =			tuple[float, float, float]
def  snake_case						(__lowercase ,      __lowercase						)	->	Tuple:

						'''simple docstring'''



						_snake_case						:					Union[str, Any]    =   end_pointa[0] - end_pointa[0]
						_snake_case						:					Any    =   end_pointa[1] - end_pointa[1]
						_snake_case						:					Tuple    =   end_pointa[2] - end_pointa[2]
						return (x, y, z)
def  snake_case						(__lowercase ,      __lowercase						)	->	Union[str, Any]:

						'''simple docstring'''



						_snake_case						:					List[str]    =   ab[1] * ac[2] - ab[2] * ac[1]  # *i
						_snake_case						:					List[str]    =   (ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
						_snake_case						:					List[str]    =   ab[0] * ac[1] - ab[1] * ac[0]  # *k
						return (x, y, z)
def  snake_case						(__lowercase ,      __lowercase						)	->	Tuple:

						'''simple docstring'''



						return tuple(round(SCREAMING_SNAKE_CASE_ ,      SCREAMING_SNAKE_CASE_						) for x in vector						) == (0, 0, 0)

def  snake_case						(__lowercase ,      __lowercase ,      __lowercase ,      __lowercase = 10						)	->	List[str]:

						'''simple docstring'''



						_snake_case						:					int    =   create_vector(SCREAMING_SNAKE_CASE_ ,      SCREAMING_SNAKE_CASE_						)
						_snake_case						:					Optional[int]    =   create_vector(SCREAMING_SNAKE_CASE_ ,      SCREAMING_SNAKE_CASE_						)
						return is_zero_vector(get_ad_vectors_cross(SCREAMING_SNAKE_CASE_ ,      SCREAMING_SNAKE_CASE_						) ,      SCREAMING_SNAKE_CASE_						)
def  snake_case						(__lowercase ,      __lowercase						)	->	str:

						'''simple docstring'''



						_snake_case						:					Tuple    =   ""
						for word_or_phrase in separated:
												if not isinstance(__lowercase ,      __lowercase						):
																		raise Exception("join() accepts only strings to be joined"						)
												joined += word_or_phrase + separator
						return joined.strip(__lowercase						)


if __name__ == "__main__":
				from doctest import testmod

				testmod()