diff --git a/Maths/VectorCrossProduct.java b/Maths/VectorCrossProduct.java new file mode 100644 index 000000000..572ba6ad0 --- /dev/null +++ b/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); + + } + +}