Pythagorean Theorem

Geometrical Definition

The dot product of two non-zero vectors u and v, is a scalar quantity that represent how much two vectors point in the same general direction. This quantity is equal to the product of their magnitudes and the cosine of the angle θ between them. The formula is:

u \cdot v = ∥ u ∥ ∥ v ∥ cos (θ)

Where:

$u$ $\cdot$ $v$ is the dot product of vectors u and v.
$∥ u ∥$ is the magnitude of vector u.
$∥ v ∥$ is the magnitudeof vector v .
$θ$ is the angle between the two vectors.

Algebraic Definition

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					class Vector2D
{
public:
    Vector2D(float, float); //constructor
    
    float X;
    float Y;
    
    Vector2D operator+(const Vector2D& other) const;
    Vector2D operator-(const Vector2D& other) const;
    Vector2D operator*(const float& scalar) const;
    Vector2D operator/(const float& scalar) const;
};

class Vector3D
{
public:
    Vector3D(float, float, float); //constructor
    
    float X;
    float Y;
    float Z;
    
    Vector3D operator+(const Vector3D& other) const;
    Vector3D operator-(const Vector3D& other) const;
    Vector3D operator*(const float scalar) const;
    Vector3D operator/(const float scalar) const;
};