Add Vector Cross Product [Fixes #2526] (#2536)

Maths/VectorCrossProduct.java

@@ -0,0 +1,124 @@
+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);
+
+    }
+
+}