====== vectorlib - functions for working with vectors ====== See the general [[courses:be5b33prg:tutorials:homeworks|homework guidelines]]! Create ''vectorlib.py'' file-library that will contain the functions listed below. Your library is going to be imported, it must work as as a library (pure functions). Optionally, include example usage of the functions within docstrings and test your module using ''[[https://docs.python.org/3/library/doctest.html|doctest]]''. The tests will not be evaluated. Vectors will be lists. You can define some auxiliary function in your library. Also think about re-using functions within other functions. If you have problems with the math backround ask your teachers or a book or wikipedia or any other math resource. Five points for the code functionality (automatic check) and two points for the code quality (readability, conciseness).


def scalar_mult(sc,v):
    """
    scalar multiplication (scalar * vector)
    :param sc: a scalar mulitplier
    :param v: a list - vector
    :return: sc * v
    """

def dot_product(u,v):
    """
    vector dot product
    :param u: a list
    :param v: a list
    :return:
    None if u and v are not compatible
    otherwise a number (float or int)
    """

def cross_product(u,v):
    """
    vector cross product, see
    :param u: a list of lenght 3
    :param v: a list of length 3
    :return:
    None if u and v are not compatible
    a list of lenght 3 - cross product of u and v
    """

def are_colinear(u,v):
    """
    testing colinearity of two vectors
    :param u: a list
    :param v: a list
    :return:
    True if u and v are colinear, False otherwise
    """

def are_perpendicular(u,v):
    """
    testing perpendicularity of two vectors
    :param u: a list
    :param v: a list
    :return:
    True if u and v are perpendicular, False otherwise
    """