#include <algorithm>
#include <cmath>
#include <iostream>
#include <iterator>
#include <numeric>
#include <string>
#include <vector>

double scalar(std::vector<double> const& u, std::vector<double> const& v)
{
    return std::inner_product(std::begin(u), std::end(u), std::begin(v), 0.0);
}

double length(std::vector<double> const& v)
{
    return std::sqrt(scalar(v, v));
}

int main()
{
    int n { };
    std::cout << "Enter dimensions: ";
    std::cin >> n;

    std::vector<double> u { };
    std::vector<double> v { };

    std::cout << "Enter u: ";
    std::copy_n(std::istream_iterator<double> { std::cin }, n, std::back_inserter(u));

    std::cout << "Enter v: ";
    std::copy_n(std::istream_iterator<double> { std::cin }, n, std::back_inserter(v));

    std::cout << "Their scalar product is: " << scalar(u, v) << std::endl;
    
    double const ulen { length(u) };
    double const vlen { length(v) };
    
    std::transform(std::begin(u), std::end(u), std::begin(u), [ulen](double e) { return e / ulen; });
    std::transform(std::begin(v), std::end(v), std::begin(v), [vlen](double e) { return e / vlen; });

    std::cout << "u = [ ";
    std::copy(std::begin(u), std::end(u), std::ostream_iterator<double>{ std::cout, " " });

    std::cout << "]" << std::endl << "v = [ ";
    std::copy(std::begin(v), std::end(v), std::ostream_iterator<double>{ std::cout, " " });
    
    std::cout << "]" << std::endl;
}