FORTRAN 90
Lecturer : Rafel Hekmat Hameed
University of Babylon
Subject : Fortran 90
College of Engineering
Year : Second B.Sc.
Mechanical Engiin
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A vector V in the plane or in space is an arrow: it is determined by its
length, denoted ȁȁ and its direction. We use vectors to represent entities which
are described by magnitude and direction. For example, a force applied at a point
is a vector: it is completely determined by the magnitude of the force and the
direction in which it is applied. An object moving in space has, at any given time,
a direction of motion, and a speed.
Magnitude of vector
Example Calculate the following:
following
ϭ
Sum
Example
Dot product
Angle between two vectors
The angle between two nonzero vectors with the same initial point is the
smallest angle between them.
Example
Ϯ
Perpendicular vector
Example
program vector_algbra
implicit none
real,dimension(3)::v,w,k
integer::i
real:: sumv,sumw,magn_v,magn_w ,dot_pro, theta
data v/5,8,-2/
data w/3,-4,1/
!compute the magnitde of two vectors
do i=1,3
sumv=sumv+v(i)**2
sumw=sumw+w(i)**2
enddo
magn_v=sqrt(sumv)
magn_w=sqrt(sumw)
write(*,50)magn_v,magn_w
50 format(2x,"magitude of vector v=",1x,e13.7,/,2x,"magitude of vector
w=",1x,e13.7)
!calculate the summation
tion of two vectors by subroutine program
call sum_vectors(v,w,k)
write(*,2)(k(i),i=1,3)
2 format(1x,3(2x, f7.4))
!calculate dot product by external function
write(*,6) dot_pro(v,w)
6 format(2x,"dot product of two vectors v&w=",f10.6)
!angle between two vectors
theta=acos(dot_pro(v,w)/(magn_v*magn_w))
ϯ
!convert theta to degree
theta=theta*180/3.14159
write(*,20)theta
20 format(2x,"angle between two vectors=",f7.3)
!check if the two vectors are perpendicular
if(dot_pro(v,w)==0)then
print*," the two vectors are perpendicular"
else
print*," the two vectors are not perpendicular"
endif
end
subroutine sum_vectors(v,w,k)
implicit none
real,dimension(3)::v,w,k
integer::i
do i=1,3
k(i)=v(i)+w(i)
enddo
end
real function dot_pro(v,w)
implicit none
real,dimension(3)::v,w
real::sum
integer::i
do i=1,3
sum=sum+v(i)*w(i)
enddo
dot_pro=sum
end
ϰ