# Vector Analysis Notes - Engineering Mathematics

## Engineering Mathematics: Vector Analysis Notes - Engineering Mathematics

The document Vector Analysis Notes - Engineering Mathematics is a part of Engineering Mathematics category.
All you need of Engineering Mathematics at this link: Engineering Mathematics
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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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