Description

Assignment 7
Hand-in via https://dtu.codejudge.net/02393-e17/assignment/
Fun with vectors The goal of the exercise is to implement a class for two dimensional vectors. Note that here “vector” refers to pairs of double values, not to the class vector of the standard C++ library. We use the mathematical notation for vectors. You are given a header-file vector2d.h (see CampusNet), that contains the declaration of the class v2d for vectors in two-dimensional space. Moreover we provide a program main.cpp file that uses the v2d class that you can use to do some tests. You should implement the class in a file vector2d.cpp as follows:
1. The constructor v2d(double a, double b) should build a vector .
2. The constructor v2d(const v2d & v) is meant to build a vector that is exactly like vector v.
3. The destructor ∼v2d() does not need to do anything special.
4. The assignment operator v2d & operator=(const v2d &v) updates a vector to make it exactly like vector v.
5. The vector addition method v2d & operator+(const v2d &v) updates a vector by adding another vector v to it. Remember that

6. The scalar multiplication method v2d & operator*(double k) updates a vector by multiplying it by a scalar factor k. Remember that scalar multiplication is defined by:

7. The scalar product method double operator*(const v2d &v) multiplies a vector by another vector v and returns the result. Remember that the scalar product of vectors is defined by

8. Method double length() computes the length of the vector. Remember that the length of a vector .
Hints
• You need to upload your file v2d.cpp only, and not the rest of the files.
• Most of the operator methods you need to implement (=, *, etc.) do not need to generate a new vector, but change the vector for which the method was called. For example, if u and v are vectors then u + v will update u (with the addition of u and v).
• Most of the operator methods you need to implement (=, *, etc.) need to return the very same vector (by reference). One of the consequences is that (u + v) + w will have the effect of updating u (with the addition of u, v and v). Recall that the object for which the object was invoked is accessed with *this. Many of your methods, hence, will need to finish with return *this; which returns the current object by reference (not a pointer!).
Challenge. Can you use templates to make class parametric with respect to the datatype of the elements (e.g. double, float, etc.)? Can you use templates to generalize the class to arbitrary dimentions (n-dimensional vectors)?
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