VECTOR CALCULUS - PowerPoint PPT Presentation

1 / 40
About This Presentation
Title:

VECTOR CALCULUS

Description:

Volume of the parallelepiped. Scalar Triple Product (contd.) Properties ... parallelepiped. Vector Triple Product. Quadruple Product of vectors ... – PowerPoint PPT presentation

Number of Views:5483
Avg rating:3.0/5.0
Slides: 41
Provided by: sla69
Category:

less

Transcript and Presenter's Notes

Title: VECTOR CALCULUS


1
VECTOR CALCULUS
Subhalakshmi Lamba
2
Vector Product
CROSS PRODUCT
3
Vector Product (contd.)
4
Vector Product (contd.)
?
  • Magnitude

5
Vector Product (contd.)
?
6
Vector Product (contd.)
?
  • Direction A rule is required !!

7
Right-Hand Rule
8
  • The order of vector multiplication
  • is important.

9
Geometrical Interpretation
10
Properties
  • Vector multiplication is not
  • Commutative.
  • Vector multiplication is Distributive
  • Multiplication by a scalar

11
Properties(contd.)
12
Properties(contd.)
Angle between them 0º
Angle between them 90º
13
Vector Product Components
?
14
Vector Product Components
15
Vector Product Components
16
Vector Product Determinant
17
Examples in Physics
The torque produced by a force is
18
Examples in Physics (contd)
The angular momentum of a particle with
respect to O
19
  • Examples in Physics (contd)

The force acting on a charged particle
moving in a magnetic field,
Positive charge
Negative charge
20
  • Applications
  • A simple cross product

21
  • An Example

C H E C K
22
  • Applications(contd.)
  • finding a unit vector
  • perpendicular to a plane.

23
  • An Example

24
SUMMARY
  • Magnitude and Direction of a vector remain
    invariant under transformation of coordinates.
  • Product of a vector with a scalar
  • Vector product directional property,
  • denotes an area.

25
  • TRIPLE PRODUCTS

26
  • Scalar Triple Product

27
  • Scalar Triple Product (contd.)

28
  • Scalar Triple Product (contd.)

29
  • Scalar Triple Product (contd.)

Area of the base
30
  • Scalar Triple Product (contd.)

Volume of the parallelepiped
31
Properties
PSUEDOSCALAR
32
Properties
  • If any two vectors of the scalar triple product
    are equal, the scalar triple
  • product is zero.

33
  • Vector Triple Product

34
An Example
35
An Example
36
An Example
What is the force that q1 exerts on q2 ?
v1
v2
B
q1
q2
r
37
An Example
v1
v2
B
q1
q2
r
38
SUMMARY
  • A physical quantity which has
  • both a magnitude and a direction
  • is represented by a vector
  • A geometrical representation
  • An analytical description components
  • Can be resolved into components along any three
    directions which are non planar.

39
SUMMARY
40
SUMMARY
  • Vector Triple Product
  • Quadruple Product of vectors
Write a Comment
User Comments (0)
About PowerShow.com