The Problem

We are going to work on making our own data structures using a C++ struct. Specifically we are going to create both data members and member functions. We are going to make a 2D MathVector struct. Keep it straight, these are the mathematical entitles called Vectors (a geometric entity with direction and magnitude).

Some Background

So if you dont remember, here is a little background on two-dimensional vectors. A vector is basically an arrow that has a magnitude (a length) and a direction (an angle with respect to typically the x axis). It usually is represented as an x,y pair, where the origin of the vector is assumed to be at 0,0 and the head of the vector is as the listed x,y pair.

Here are some of the operations you can perform on your new MathVector struct.

MathVector addition. If V1 is (x,y) and V2 is (a,b), the V+W is (x+a,y+b), a MathVector

MathVector multiplication by a scalar integer type. If V1 is (x,y), then V*n is (x*n,y*n),

returning a new MathVector

MathVector multiplication with another MathVector. There are two possibilities, dot

product or cross product. Well do dot product. If V=(x,y) and W=(a,b), then V*W = x*a +

y*b, a scalar. Thus the dot product returns a scalar type long, not a MathVector

MathVector magnitude. The magnitude based on the Pythagorean theorem for a V=(x,y) says that

the magnitude is sqrt(x^2 + y^2). Your Tasks

Make a MathVector struct. Data members are: longx

longy Constructors are:

default constructor

two args, each a long, constructor: first arg is the x value, the second is the y value. No defaults. The member functions are:

MathVector add(const MathVector&). Single arg a const ref to MathVector. Adds two MathVectors as described. Returns a new MathVector.

A vector V + W V-W Here are some of the operations you can perform on your new MathVector struct.

V

MathVector mult(long). Multiplies a single MathVector element by a long as described. Returns a new MathVector.

long mult(const MathVector&). Single arg a const ref to MathVector . Multiplies the two MathVectors as a dot product, yielding a long as described above.

double magnitude(). No args. Calculate the magnitude of the MathVector as described. Returns a double.

Make the following regular function (not a member)

string vec_to_str(const MathVector &v). No args, returns a string representation

of the Vector in the format: "x:y" Make a vector.h and a vector.cpp to store your MathVector struct. Compile it with the

main.cpp that is in the lab directory and run.

Main.cpp:

#include #include using std::cout; using std::endl; using std::string; #include "vector.h" int main (){ long scalar=20; MathVector v1; MathVector v2(3,2); long long_result; double dbl_result; MathVector vec_result; cout   V4V42*V V4W V4W xy W W  W 0.0 A vector V+ W V-W V *2