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## VECTOR CALCULUS

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

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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