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Fall 2006 
Page 2


Fall 2006 
Scalar Quantity 
(mass, speed, voltage, current and power) 
1- Real number (one variable) 
  
2- Complex number (two variables) 
Vector Algebra 
(velocity, electric field and magnetic field) 
Magnitude & direction 
1- Cartesian (rectangular) 
2- Cylindrical 
3- Spherical 
Specified by one of the following 
coordinates best applied to application: 
Page 101 
Page 3


Fall 2006 
Scalar Quantity 
(mass, speed, voltage, current and power) 
1- Real number (one variable) 
  
2- Complex number (two variables) 
Vector Algebra 
(velocity, electric field and magnetic field) 
Magnitude & direction 
1- Cartesian (rectangular) 
2- Cylindrical 
3- Spherical 
Specified by one of the following 
coordinates best applied to application: 
Page 101 
Conventions 
• Vector quantities denoted as    or v 
• We will use column format vectors: 
 
 
 
 
• Each vector is defined with respect to a set of 
basis vectors (which define a co-ordinate 
system). 
v
?
[ ] [ ] ( )
T
v v v v v v
v
v
v
3 2 1 3 2 1
3
2
1
= ?
?
?
?
?
?
?
?
?
?
?
= v
Page 4


Fall 2006 
Scalar Quantity 
(mass, speed, voltage, current and power) 
1- Real number (one variable) 
  
2- Complex number (two variables) 
Vector Algebra 
(velocity, electric field and magnetic field) 
Magnitude & direction 
1- Cartesian (rectangular) 
2- Cylindrical 
3- Spherical 
Specified by one of the following 
coordinates best applied to application: 
Page 101 
Conventions 
• Vector quantities denoted as    or v 
• We will use column format vectors: 
 
 
 
 
• Each vector is defined with respect to a set of 
basis vectors (which define a co-ordinate 
system). 
v
?
[ ] [ ] ( )
T
v v v v v v
v
v
v
3 2 1 3 2 1
3
2
1
= ?
?
?
?
?
?
?
?
?
?
?
= v
Unit vector 
Magnitude 
+
+
+ +
+ +
= =
+ + = =
+ + =
2 2 2
2 2 2
ˆ ˆ ˆ
ˆ
ˆ ˆ ˆ
z y x
z y x
z y x
z y x
A A A
A z A y A x
A
A
a
A A A A A
A z A y A x A
?
?
?
Page 101-102 
a ˆ
Page 5


Fall 2006 
Scalar Quantity 
(mass, speed, voltage, current and power) 
1- Real number (one variable) 
  
2- Complex number (two variables) 
Vector Algebra 
(velocity, electric field and magnetic field) 
Magnitude & direction 
1- Cartesian (rectangular) 
2- Cylindrical 
3- Spherical 
Specified by one of the following 
coordinates best applied to application: 
Page 101 
Conventions 
• Vector quantities denoted as    or v 
• We will use column format vectors: 
 
 
 
 
• Each vector is defined with respect to a set of 
basis vectors (which define a co-ordinate 
system). 
v
?
[ ] [ ] ( )
T
v v v v v v
v
v
v
3 2 1 3 2 1
3
2
1
= ?
?
?
?
?
?
?
?
?
?
?
= v
Unit vector 
Magnitude 
+
+
+ +
+ +
= =
+ + = =
+ + =
2 2 2
2 2 2
ˆ ˆ ˆ
ˆ
ˆ ˆ ˆ
z y x
z y x
z y x
z y x
A A A
A z A y A x
A
A
a
A A A A A
A z A y A x A
?
?
?
Page 101-102 
a ˆ
Vectors 
• Vectors represent directions 
– points represent positions 
 
• Both are meaningless 
without reference to a 
coordinate system 
– vectors require a set of basis 
vectors 
– points require an origin and a 
vector space 
?
?
?
?
?
?
=
?
?
?
?
?
?
=
y
x
y
x
v
v
v
v
P v
both vectors equal 
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FAQs on Vector Analysis - Engineering Mathematics - Civil Engineering (CE)

1. What is vector analysis?
Ans. Vector analysis is a branch of mathematics that deals with the study and manipulation of vectors, which are quantities that have both magnitude and direction. It involves various operations such as addition, subtraction, dot product, cross product, and differentiation and integration of vector functions.
2. What are the applications of vector analysis?
Ans. Vector analysis finds applications in various fields such as physics, engineering, computer graphics, and fluid dynamics. It is used to analyze forces, velocities, and accelerations in mechanics, solve problems related to electric and magnetic fields in electromagnetism, and model fluid flow in fluid dynamics.
3. What are the basic operations involved in vector analysis?
Ans. The basic operations involved in vector analysis include addition, subtraction, scalar multiplication, dot product, and cross product. Addition and subtraction are used to combine or break down vectors, scalar multiplication scales the magnitude of a vector, dot product measures the similarity between two vectors, and cross product gives a vector perpendicular to the plane formed by two vectors.
4. How is vector analysis different from scalar analysis?
Ans. Vector analysis deals with quantities that have both magnitude and direction, whereas scalar analysis deals with quantities that have only magnitude. In vector analysis, the operations involve vectors and yield vectors, while in scalar analysis, the operations involve scalars and yield scalars. Vector analysis is more suitable for analyzing physical quantities with direction, such as force and velocity.
5. Can vector analysis be applied to three-dimensional space?
Ans. Yes, vector analysis can be applied to three-dimensional space. In three dimensions, vectors are represented by three components (x, y, z) and the operations of vector analysis are extended accordingly. The concepts of dot product, cross product, and vector differentiation and integration can be generalized to three dimensions, allowing the analysis of vector quantities in three-dimensional space.
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