In [7]:

    

from math import sqrt


def vector_add(v, w):
    '''adds corresponding elements of vectors'''
    return [v_i + w_i for v_i,w_i in zip(v, w)]


def vector_subtract(v, w):
    '''subtract corresponding elements of vectors'''
    return [v_i - w_i for v_i,w_i in zip(v, w)]


def vector_sum(vectors):
    '''sum all corresponding elements'''
    result = vectors[0]
    for vector in vectors[1:]:
        result = vector_add(result, vector)

    return result


def vector_sum_fast(vectors):
    '''sum all corresponding elements'''
    return reduce(vector_add, vectors)


def scalar_multiply(c, vector):
    '''c is the scalar'''
    return [c * v_i for v_i in vector]


def vector_mean(vectors):
    '''The ith element of the result is the mean of the ith element
    of all the input vectors.'''
    n = len(vectors)
    return scalar_multiply(1/n, vector_sum(vectors))


def dot(v, w):
    '''the sum of the product of the matching elements
    of the input vectors'''
    return sum(v_i * w_i for v_i,w_i in zip(v, w))


def sum_of_squares(v):
    '''add the square of each element'''
    return dot(v, v)


def magnitude(v):
    '''Find the length of a vector in cartesian space'''
    return sqrt(sum_of_squares(v))


def distance(v, w):
    '''Find the distance between two vectors'''
    return magnitude(vector_subtract(v, w))


a = [0, 5, 5]
b = [2, 5, 7]
distance(a, b)


    

    
Out[7]:





2.8284271247461903

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