使用类在C++中实现矢量数量

向量数量是同时具有大小和方向的数量。在这里，数量级只是数量的数量或大小，方向是数量的前进方向。例如，考虑语句“向北20英里”。在上面的陈述中，20是震级，而North是方向。

例子：

Input : Store and display vector with components 3, 4, 5.
Output : 3i + 4j + 5k

Input : Dot Product for V1 = (1, 3, 5), V2 = (2, 3, 0)
Output : 11

where i, j, k are unit vectors in x, y and z directions respectively.

通常，向量表示为：

V = Xi + Yj + Zk

Where, X, Y and Z are the magnitude of the vector V in the directions i , j and k respectively.

可以在Vector上执行的各种操作：

1. 向量的相加：向量的相加是通过将两个向量的相应X，Y和Z量值相加而得到的。
   例子：
   v1 = 1i + 2j + 3k
   v2 = 3i + 2j + 1k
   因此，结果向量v = v1 + v2 = 4i + 4j + 4k
2. 向量的点积：两个向量v1和v2的点积计算如下：

   v = v1 . v2
     = magnitude(v1)*magnitude(v2)*Cos(θ)
   
   Where, θ is the angle between the vectors v1 and v2.
   

   例子：
   v1 = 1i + 2j + 3k
   v2 = 3i + 2j + 1k
   因此，v = v1。 v2 = 3 + 4 + 3 = 10

3. 向量的叉积：向量的叉积是通过使用行列式为向量A = AXI + AYJ + AZK且b = BXI + BYJ + BZK完成

   c = a X b = i(ay * bz – by * az)– j(ax * bz – az * bx)+ k(ax * by – bx * ay)

   例子：
   v1 = 3i + 4j + 2k
   v2 = 6i + 3j + 9k
   因此，v = v1 X v2 = 30i – 15j – 15k

下面是在C++中使用类的上述操作的实现：

#include 
#include 
using namespace std;
  
class Vector {
private:
    int x, y, z;
    // Components of the Vector
  
public:
    Vector(int x, int y, int z)
    {
        // Constructor
        this->x = x;
        this->y = y;
        this->z = z;
    }
    Vector operator+(Vector v); // ADD 2 Vectors
    Vector operator-(Vector v); // Subtraction
    int operator^(Vector v); // Dot Product
    Vector operator*(Vector v); // Cross Product
    float magnitude()
    {
        return sqrt(pow(x, 2) + pow(y, 2) + pow(z, 2));
    }
    friend ostream& operator<<(ostream& out, const Vector& v);
    // To output the Vector
};
  
// Addition of vectors
Vector Vector::operator+(Vector v)
{
    int x1, y1, z1;
    x1 = x + v.x;
    y1 = y + v.y;
    z1 = z + v.z;
    return Vector(x1, y1, z1);
}
  
// Subtraction of vectors
Vector Vector::operator-(Vector v)
{
    int x1, y1, z1;
    x1 = x - v.x;
    y1 = y - v.y;
    z1 = z - v.z;
    return Vector(x1, y1, z1);
}
  
// Dot product of vectors
int Vector::operator^(Vector v)
{
    int x1, y1, z1;
    x1 = x * v.x;
    y1 = y * v.y;
    z1 = z * v.z;
    return (x1 + y1 + z1);
}
  
// Cross product of vectors
Vector Vector::operator*(Vector v)
{
    int x1, y1, z1;
    x1 = y * v.z - z * v.y;
    y1 = z * v.x - x * v.z;
    z1 = x * v.y - y * v.x;
    return Vector(x1, y1, z1);
}
  
// Display Vector
ostream& operator<<(ostream& out, const Vector& v)
{
    out << v.x << "i ";
    if (v.y >= 0)
        out << "+ ";
    out << v.y << "j ";
    if (v.z >= 0)
        out << "+ ";
    out << v.z << "k" << endl;
    return out;
}
  
// Driver program
int main()
{
    // Let us Take the vector quantites :
    // V1 = 3i + 4j + 2k
    // V2 = 6i + 3j + 9k
    Vector V1(3, 4, 2), V2(6, 3, 9);
  
    cout << "V1 = " << V1;
    cout << "V2 = " << V2;
  
    cout << "V1 + V2 = " << (V1 + V2);
    cout << "Dot Product is : " << (V1 ^ V2);
    cout << "Cross Product is : " << (V1 * V2);
  
    return 0;
}

输出：

V1 = 3i + 4j + 2k
V2 = 6i + 3j + 9k
V1 + V2 = 9i + 7j + 11k
Dot Product is : 48Cross Product is : 30i -15j -15k

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