Presentation is loading. Please wait.

Presentation is loading. Please wait.

VECTOR CALCULUS. Vector Multiplication b sin   A = a  b Area of the parallelogram formed by a and b.

Published byAmberlynn Park Modified over 9 years ago

Similar presentations

Presentation on theme: "VECTOR CALCULUS. Vector Multiplication b sin   A = a  b Area of the parallelogram formed by a and b."— Presentation transcript:

1 VECTOR CALCULUS

2 Vector Multiplication b sin   A = a  b Area of the parallelogram formed by a and b

3 a b Right-Hand Rule

4 Properties Vector multiplication is not Commutative. Vector multiplication is Distributive Multiplication by a scalar

5 Properties Angle between them 0º Angle between them =90º j i k

6 Vector Product: Components  

7

8 Example z x y The torque produced by a force is

9 SUMMARY Magnitude and Direction of a vector remain invariant under transformation of coordinates Vector product : directional property, denotes an area. Scalar product a. b = a x b x + a y b y + a z b z

Download ppt "VECTOR CALCULUS. Vector Multiplication b sin   A = a  b Area of the parallelogram formed by a and b."

Similar presentations

10.2 Vectors and Vector Value Functions

10.2 Vectors and Vector Value Functions
CE 201 - Statics Lecture 2. Contents Vector Operations – Multiplication and Division of Vectors – Addition of Vectors – Subtraction of vectors – Resolution.

CE Statics Lecture 2. Contents Vector Operations – Multiplication and Division of Vectors – Addition of Vectors – Subtraction of vectors – Resolution.
Lesson 6-3 The Scalar Product AP Physics C. 6 – 3 The scalar product, or dot product, is a mathematical operation used to determine the component of a.

Lesson 6-3 The Scalar Product AP Physics C. 6 – 3 The scalar product, or dot product, is a mathematical operation used to determine the component of a.
Vectors and the Geometry of Space 9. The Cross Product 9.4.

Vectors and the Geometry of Space 9. The Cross Product 9.4.
1 Chapter Two Vectors. 2 A quantity consisting only of magnitude is called a scalar quantity. A quantity that has both magnitude and direction and obeys.

1 Chapter Two Vectors. 2 A quantity consisting only of magnitude is called a scalar quantity. A quantity that has both magnitude and direction and obeys.
The Scalar or Dot Product Lecture V1.2 Example 4 Moodle.

The Scalar or Dot Product Lecture V1.2 Example 4 Moodle.
10.5 The Dot Product. Theorem Properties of Dot Product If u, v, and w are vectors, then Commutative Property Distributive Property.

10.5 The Dot Product. Theorem Properties of Dot Product If u, v, and w are vectors, then Commutative Property Distributive Property.
Vectors in Two and Three Dimensions. Definition A vector is a quantity that is determined by a magnitude and a direction.

Vectors in Two and Three Dimensions. Definition A vector is a quantity that is determined by a magnitude and a direction.
Phy 212: General Physics II Chapter : Topic Lecture Notes.

Phy 212: General Physics II Chapter : Topic Lecture Notes.
The Vector or Cross Product Lecture V1.3 Example 5 Moodle.

The Vector or Cross Product Lecture V1.3 Example 5 Moodle.
Vector Products (Cross Product). Torque F r T F r T F1F1 F2F2.

Vector Products (Cross Product). Torque F r T F r T F1F1 F2F2.
16.360 Lecture 13 Today Basic Laws of Vector Algebra Scalars: e.g. 2 gallons, $1,000, 35ºC Vectors: e.g. velocity: 35mph heading south 3N force toward.

Lecture 13 Today Basic Laws of Vector Algebra Scalars: e.g. 2 gallons, $1,000, 35ºC Vectors: e.g. velocity: 35mph heading south 3N force toward.
Lecture 1eee3401 Chapter 2. Vector Analysis 2-2, 2-3, Vector Algebra (pp. 11-19) Scalar: has only magnitude (time, mass, distance) A,B Vector: has both.

Lecture 1eee3401 Chapter 2. Vector Analysis 2-2, 2-3, Vector Algebra (pp ) Scalar: has only magnitude (time, mass, distance) A,B Vector: has both.
Vectors Sections 6.6. Objectives Rewrite a vector in rectangular coordinates (in terms of i and j) given the initial and terminal points of the vector.

Vectors Sections 6.6. Objectives Rewrite a vector in rectangular coordinates (in terms of i and j) given the initial and terminal points of the vector.
Physics 106: Mechanics Lecture 05 Wenda Cao NJIT Physics Department.

Physics 106: Mechanics Lecture 05 Wenda Cao NJIT Physics Department.
Vector Torque. Direction of Angular Velocity  Angular velocity can be clockwise or counterclockwise around the axis of rotation.  It has magnitude and.

Vector Torque. Direction of Angular Velocity  Angular velocity can be clockwise or counterclockwise around the axis of rotation.  It has magnitude and.
Example: Determine the angle between the vectors A and B.

Example: Determine the angle between the vectors A and B.
Vector Product Results in a vector.

Vector Product Results in a vector.
Three-Dimensional Forces Systems: Rectangular Components

Three-Dimensional Forces Systems: Rectangular Components
8.6.1 – The Dot Product (Inner Product). So far, we have covered basic operations of vectors – Addition/Subtraction – Multiplication of scalars – Writing.

8.6.1 – The Dot Product (Inner Product). So far, we have covered basic operations of vectors – Addition/Subtraction – Multiplication of scalars – Writing.

Similar presentations

Ads by Google