Vectors What are they? How do we measure them? How do we add them? How do we scalar multiply them?

Slides:

Advertisements

Similar presentations

10.2 Vectors and Vector Value Functions

Advertisements

Vectors Lesson 4.3.

Introduction to Vectors March 2, What are Vectors? Vectors are pairs of a direction and a magnitude. We usually represent a vector with an arrow:

Phy 212: General Physics II Chapter : Topic Lecture Notes.

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.

PHY 1151 Principles of Physics I

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: 5 Minute Review Vectors can be added or subtracted. ◦ To add vectors graphically, draw one after the other, tip to tail. ◦ To add vectors algebraically,

Vectors: 5 Minute Review Vectors can be added or subtracted. ◦ To add vectors graphically, draw one after the other, tip to tail. ◦ To add vectors algebraically,

Vectors. 2 Scalars and Vectors A scalar is a single number that represents a magnitude –E.g. distance, mass, speed, temperature, etc. A vector is a set.

12.9 Parallel & Perpendicular Vectors in Two Dimensions

APPLICATIONS OF TRIGONOMETRY

Section 13.3 The Dot Product. We have added and subtracted vectors, what about multiplying vectors? There are two ways we can multiply vectors 1.One results.

2009 Physics 2111 Fundamentals of Physics Chapter 3 1 Fundamentals of Physics Chapter 3 Vectors 1.Vectors & Scalars 2.Adding Vectors Geometrically 3.Components.

3-2 Vectors and Scalars  Is a number with units. It can be positive or negative. Example: distance, mass, speed, Temperature… Chapter 3 Vectors  Scalar.

Section 13.4 The Cross Product. Torque Torque is a measure of how much a force acting on an object causes that object to rotate –The object rotates around.

Vectors 7.4 JMerrill, 2007 Revised Definitions Vectors are quantities that are described by direction and magnitude (size). Example: A force is.

Vectors. Vectors: magnitude and direction Practice.

Algebraic Vectors Section 8-2. WHAT YOU WILL LEARN: 1.How to find ordered pairs that represent vectors. 2.How to add, subtract, multiply and find the.

2-D motion (no projectiles – yet) Physics Chapter 3 section 1 Pages

Unit 2 1-Dimensional Kinematics

Vectors. He takes off from Philadelphia International Airport He flies 20 miles North He then flies 10 miles at a heading 80° East of North Distance =

Vectors. Distance versus Displacement A ferry boat captain and a truck driver are asked how far it is from Vectorville to Component Cove.

Assigned work: pg.377 #5,6ef,7ef,8,9,11,12,15,16 Pg. 385#2,3,6cd,8,9-15 So far we have : Multiplied vectors by a scalar Added vectors Today we will: Multiply.

Section 11.4 The Cross Product Calculus III September 22, 2009 Berkley High School.

Advanced Precalculus Notes 8.5 The Dot Product The dot product of two vectors is a scalar: If v = 2i – 3j and w = 5i + 3j find: a) v ∙ wb) w ∙ vc) v ∙

Meeting 23 Vectors. Vectors in 2-Space, 3-Space, and n- Space We will denote vectors in boldface type such as a, b, v, w, and x, and we will denote scalars.

Vectors Physics Book Sections Two Types of Quantities SCALAR Number with Units (MAGNITUDE or size) Quantities such as time, mass, temperature.

1.1 Scalars & Vectors Scalar & Vector Quantities Scalar quantities have magnitude only. ex. Volume, mass, speed, temperature, distance Vector quantities.

Vectors and Dot Product 6.4 JMerrill, Quick Review of Vectors: Definitions Vectors are quantities that are described by direction and magnitude.

VECTORS Dr. Shildneck. Vectors There are two types of quantities in the world. Scalar – a quantity that is specified by a single value with an appropriate.

Vectors and Vector Addition. Vectors vs. Scalars Scalars are physical quantities having only magnitude– that is, a numerical value & units. Ex: a speed.

Objectives: Graph vectors in 3 dimensions Use cross products and dot products to find perpendicular vectors.

The definition of the product of two vectors is: This is called the dot product. Notice the answer is just a number NOT a vector.

I know where I’m going. A scalar is a quantity described by just a number, usually with units. It can be positive, negative, or zero. Examples: –Distance.

Math /7.5 – Vectors 1. Suppose a car is heading NE (northeast) at 60 mph. We can use a vector to help draw a picture (see right). 2.

Vectors and Dot Products OBJECTIVES: Find the dot product of two vectors and use the properties of the dot product. Find the angle between two vectors.

C H. 6 – A DDITIONAL T OPICS IN T RIGONOMETRY 6.4 – Dot Products.

Algebraic Properties Terra Alta/East Preston School Terra Alta, West Virginia.

Vectors Def. A vector is a quantity that has both magnitude and direction. v is displacement vector from A to B A is the initial point, B is the terminal.

Vectors Def. A vector is a quantity that has both magnitude and direction. v is displacement vector from A to B A is the initial point, B is the terminal.

Elementary Linear Algebra

Enduring Understanding: Modeling is widely used to represent physical and kinematic information. Essential Question: What are the practical applications.

Multiplying 2 Digit Factors

Scalar Vector speed, distance, time, temperature, mass, energy

How do we add and subtract vectors?

Work – review from gr 11 Units - Joules (J) = Nm = kgm2s-2

Vectors What is a vector?.

Algebraic Properties.

VECTOR AND SCALAR QUANTITIES.

Scalars vs. Vectors.

Enduring Understanding: Modeling is widely used to represent physical and kinematic information. Essential Question: What are the practical applications.

Vectors, Linear Combinations and Linear Independence

Representing Motion.

Only some of this is review.

Vectors More math concepts.

VECTORS © John Parkinson.

THE DOT PRODUCT.

Vectors Vectors are a way to describe motion that is not in a straight line. All measurements can be put into two categories: Scalars = magnitude Vectors.

Vectors An Introduction.

Unit 1: Intro to Physics Scalars & Vectors.

Distances and displacements

Aim: How do we add vectors graphically?

Ch. 15- Vectors in 2-D.

Properties A property is something that is true for all situations.

Where and When Section 2-2.

Presentation transcript:

Vectors What are they? How do we measure them? How do we add them? How do we scalar multiply them?

What is a vector? Def. A vector is a magnitude and direction in space. Direction: Northeast; Magnitude: ? Direction: ? ; Magnitude: ? Direction: North ; Magnitude: 1 Inch tail head

Adding vectors EX 1: Start at the desk.. 1.Go West for 2 feet. 2.Go North 5 feet. How far have you traveled? How far are you from where you started? EX2: EX3:

Adding vectors

Subtracting vectors Home School CSUN

Zero Vector & Scalar Multiplication Home School CSUN

Exercises

200nts

Exercises: Homework

Algebraic Approach

Addition: Algebraic Approach

Magnitude: Algebraic Approach

A little work with physics The tractor is dead. Turtle pulls the tractor. The “work” done depends on the direction and magnitude of the pull (force) as well as the distance traveled.

More Work: (measures something about how a force vector acts on an object moving in a fixed direction)

Dot Product

Properties of dot product: