package Maths;

/**

* @file

*

* @brief Calculates the [Cross Product](https://en.wikipedia.org/wiki/Cross_product) and the magnitude of two mathematical 3D vectors.

*

*

* @details Cross Product of two vectors gives a vector.

* Direction Ratios of a vector are the numeric parts of the given vector. They are the tree parts of the

* vector which determine the magnitude (value) of the vector.

* The method of finding a cross product is the same as finding the determinant of an order 3 matrix consisting

* of the first row with unit vectors of magnitude 1, the second row with the direction ratios of the

* first vector and the third row with the direction ratios of the second vector.

* The magnitude of a vector is it's value expressed as a number.

* Let the direction ratios of the first vector, P be: a, b, c

* Let the direction ratios of the second vector, Q be: x, y, z

* Therefore the calculation for the cross product can be arranged as:

*

* ```

* P x Q:

* 1 1 1

* a b c

* x y z

* ```

*

* The direction ratios (DR) are calculated as follows:

* 1st DR, J: (b * z) - (c * y)

* 2nd DR, A: -((a * z) - (c * x))

* 3rd DR, N: (a * y) - (b * x)

*

* Therefore, the direction ratios of the cross product are: J, A, N

* The following Java Program calculates the direction ratios of the cross products of two vector.

* The program uses a function, cross() for doing so.

* The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.

*

* Magnitude of a vector is the square root of the sum of the squares of the direction ratios.

*

*

* For maintaining filename consistency, Vector class has been termed as VectorCrossProduct

*

* @author [Syed](https://github.com/roeticvampire)

*/

public class VectorCrossProduct {

int x;

int y;

int z;

//Default constructor, initialises all three Direction Ratios to 0

VectorCrossProduct(){

x=0;

y=0;

z=0;

}

/**

* constructor, initialises Vector with given Direction Ratios

* @param _x set to x

* @param _y set to y

* @param _z set to z

*/

VectorCrossProduct(int _x,int _y, int _z){

x=_x;

y=_y;

z=_z;

}

/**

* Returns the magnitude of the vector

* @return double

*/

double magnitude(){

return Math.sqrt(x*x +y*y +z*z);

}

/**

* Returns the dot product of the current vector with a given vector

* @param b: the second vector

* @return int: the dot product

*/

int dotProduct(VectorCrossProduct b){

return x*b.x + y*b.y +z*b.z;

}

/**

* Returns the cross product of the current vector with a given vector

* @param b: the second vector

* @return vectorCrossProduct: the cross product

*/

VectorCrossProduct crossProduct(VectorCrossProduct b){

VectorCrossProduct product=new VectorCrossProduct();

product.x = (y * b.z) - (z * b.y);

product.y = -((x * b.z) - (z * b.x));

product.z = (x * b.y) - (y * b.x);

return product;

}

/**

* Display the Vector

*/

void displayVector(){

System.out.println("x : "+x+"\ty : "+y+"\tz : "+z);

}

public static void main(String[] args) {

test();

}

static void test(){

//Create two vectors

VectorCrossProduct A=new VectorCrossProduct(1,-2,3);

VectorCrossProduct B=new VectorCrossProduct(2,0,3);

//Determine cross product

VectorCrossProduct crossProd=A.crossProduct(B);

crossProd.displayVector();

//Determine dot product

int dotProd=A.dotProduct(B);

System.out.println("Dot Product of A and B: "+dotProd);

}

}