Calculate the Cross Product of Two Vectors

This is a part of the student software manual project for Math 5610: Computational Linear Algebra and Solution of Systems of Equations.

Routine Name: vec_cross_prod3

Author: Christian Bolander

Language: Fortran. This code can be compiled using the GNU Fortran compiler by $ gfortran -c vec_cross_prod3.f90

and can be added to a program using

$ gfortran program.f90 vec_cross_prod3.o

Description/Purpose: This routine will calculate the cross product of two vectors, a and b of length 3, using

Input:

a : REAL - an arbitrary vector of length 3

b : REAL - an arbitrary vector of length 3

Output:

crossprod : REAL - the cross product of a and b (a vector of length 3)

Usage/Example:

This routine can be implemented in a program as follows

a = (/2.D0, 3.D0, 4.D0/)
b = (/5.D0, 6.D0, 7.D0/)
CALL vec_cross_prod3(a, b, crossprod)
WRITE(*,*) crossprod

The output from the above code:

  -3.0000000000000000        6.0000000000000000       -3.0000000000000000 

which is the vector cross product of a and b.

Implementation/Code: The code for vec_cross_prod3 can be seen below.

SUBROUTINE vec_cross_prod3(a, b, crossprod)
	IMPLICIT NONE
	
	! I/O variable initiation
	REAL*8, INTENT(IN) :: a(1:3), b(1:3)
	REAL*8, INTENT(OUT) :: crossprod(1:3)
	
	! Calculate the cross product for two vectors of length 3.
	crossprod(1) = a(2)*b(3) - a(3)*b(2)
	crossprod(2) = -(a(1)*b(3) - a(3)*b(1))
	crossprod(3) = a(1)*b(2) - a(2)*b(1)
END SUBROUTINE