vectors

University of Babylon Lecture: Roaya Mahmood Jaleel
faculty of Engineering Subject: Mathematics
Department of Chemical Engineering Stage : 2nd stage
1
vectors
Some of the things we measure are determined simply by their magnitudes. To record mass, length, or time, for example, we need only write down a number and name an appropriate unit of measure. We need more information to describe a force, displacement, or velocity. To describe a force, we need to record the direction in which it acts as well as how large it is. To describe a body’s displacement, we have to say in what direction it moved as well as how far. To describe a body’s velocity, we have to know where the body is headed as well as how fast it is going.
Vector is a quantity having booth magnitude and direction , such as Displacement , velocity , acceleration.
Graphically
Fundamental of vector
Components of vector
V= AC
University of Babylon Lecture: Roaya Mahmood Jaleel
faculty of Engineering Subject: Mathematics
Department of Chemical Engineering Stage : 2nd stage
2
V= ai + bj
Vectors Alggebra
Addition
If v1= a1i + b2j , v2= a2i + b2j
v1 + v2 = (a1 + a2)i + (b1+ b2)j
EXAMPLE 1:
(2i+4j) + (5i+3j) = (2+5)i +(4+3)j
V= 7i+7j
Subtraction
If v1= a1i - b2j , v2= a2i - b2j
v1 - v2 = (a1 - a2)i + (b1- b2)j
EXAMPLE2:
v1= 6i + 2j , v2= 3i-5j
v1 - v2 = ( 6- 3)i + (2-(-5))j v1 - v2 = 3i + 7j
A
C
BC