Question

C++:

vectors. Euclidean vectors are sets of values which represent values in a dimensional field. A 2d vector would represent values in x,y space (an ordered pair of coordinates) and a 3d vector would represent values in x,y,z space (an ordered triplet of coordinates). We define the basic definition of the 2d vector as follows:

class Vector2D {

public: Vector2D ();

Vector2D (double ,double );

double dotProduct(Vector2D& );

friend Vector2D& operator +(Vector2D&, Vector2D&);

friend std::ostream& operator <<(std::ostream& o, Vector2D& a);

private:

double magnitude,angle, x, y; };

We continue by implementing this class.

Constructors and member functions (methods):

1)We would like to define two ways to create a 2d vector and a behavior involving two vectors.

(a) First, write the implementation for the default constructor. It should set all the class attributes to the value 0.

(b) Second, write the implementation for the ‘double, double’ constructor. The constructor is given values for the magnitude and angle (in radians) as its parameters. It should set the private variables to those values and calculate the x and y values. The value of x should be the magnitude multiplied by the cosine of the angle (in degrees). The value of y should be the magnitude multiplied by the sine of the angle (in degrees). You can convert between radians and degrees by multiplying the number of radians by 180 and dividing by pi.

(c) Lastly, we write the implementation for the dot product method. The formula for calculating the dot product of two vectors a = {ax, ay} and b = {bx, by} is ax ∗ bx + ay ∗ by.