In C#, vectors can be represented using arrays or collections, but for a more mathematical and object-oriented approach, you
can define a
`Vector` class that encapsulates vector operations like addition, subtraction, dot product, etc. Below is a basic implementation of a 2D vector
class in C#:
```csharp
using System;
public class Vector2
{
public float X { get; set; }
public float Y { get; set; }
public Vector2(float x, float y)
{
X = x;
Y = y;
}
// Vector addition
public static Vector2 operator +(Vector2 v1, Vector2 v2)
{
return new Vector2(v1.X + v2.X, v1.Y + v2.Y);
}
// Vector subtraction
public static Vector2 operator -(Vector2 v1, Vector2 v2)
{
return new Vector2(v1.X - v2.X, v1.Y - v2.Y);
}
// Scalar multiplication
public static Vector2 operator *(Vector2 v, float scalar)
{
return new Vector2(v.X * scalar, v.Y * scalar);
}
// Dot product
public static float Dot(Vector2 v1, Vector2 v2)
{
return v1.X * v2.X + v1.Y * v2.Y;
}
// Magnitude (Length) of the vector
public float Magnitude()
{
return (float)Math.Sqrt(X * X + Y * Y);
}
// Normalize the vector
public Vector2 Normalize()
{
float magnitude = Magnitude();
return new Vector2(X / magnitude, Y / magnitude);
}
// Override ToString for easy printing
public override string ToString()
{
return $"({X}, {Y})";
}
}
class Program
{
static void Main(string[] args)
{
Vector2 v1 = new Vector2(3, 4);
Vector2 v2 = new Vector2(1, 2);
Vector2 sum = v1 + v2;
Vector2 difference = v1 - v2;
Vector2 scaled = v1 * 2;
float dotProduct = Vector2.Dot(v1, v2);
Vector2 normalized = v1.Normalize();
Console.WriteLine($"v1: {v1}");
Console.WriteLine($"v2: {v2}");
Console.WriteLine($"Sum: {sum}");
Console.WriteLine($"Difference: {difference}");
Console.WriteLine($"Scaled v1: {scaled}");
Console.WriteLine($"Dot Product: {dotProduct}");
Console.WriteLine($"Normalized v1: {normalized}");
}
}
```
### Explanation:
- **Vector2 Class:** This represents a 2D vector with `X` and `Y` components.
- **Operator Overloading:** The `+`, `-`, and `*` operators are overloaded to support vector addition, subtraction, and scalar multiplication.
- **Dot Product:** A static method to calculate the dot product of two vectors.
- **Magnitude:** This method returns the length of the vector.
- **Normalize:** Returns a unit vector (vector with a magnitude of 1) in the same direction.
### Usage:
- You can create instances of the `Vector2` class, perform operations like addition, subtraction, scaling, etc., and easily print the results.
This can be extended to 3D vectors by adding a `Z` component and modifying the methods accordingly.
