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 don't 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 a new `MathVector` with the values (x + a, y + b)
- `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. We'll 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 V = (x, y), the magnitude is sqrt(x^2 + y^2)
v Your Tasks
Make a `MathVector struct`. Data members are:
- `long x`
- `long y`
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`.
- `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 `MathVector` in the format: "x:y"
