Vectors Lesson 13.4 Pre-AP Geometry. Lesson Focus This lesson defines the concept of a vector. Vectors have important applications in physics, engineering,

Slides:

Advertisements

Similar presentations

6.3 Vectors in the plane Day 1 Objectives: - define vectors

Advertisements

10.2 Vectors and Vector Value Functions

6.3 Vectors in the Plane Many quantities in geometry and physics, such as area, time, and temperature, can be represented by a single real number. Other.

General Physics (PHYS101)

55: The Vector Equation of a Plane

Chapter 7: Vectors and the Geometry of Space

DOT PRODUCT (Section 2.9) Today’s Objective:

Digital Lesson Vectors.

6.3 Vectors in the Plane Day Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 A ball flies through the air at a certain speed.

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.

Scalar and Vector Fields

Geometry of R 2 and R 3 Vectors in R 2 and R 3. NOTATION RThe set of real numbers R 2 The set of ordered pairs of real numbers R 3 The set of ordered.

UNIT 1 VECTORS. SECTION 1.1 VECTOR CONCEPTS A vector is a mathematical object with both MAGNITUDE (size) and DIRECTION.

POSITION VECTORS & FORCE VECTORS

Physics 203 – College Physics I Department of Physics – The Citadel Physics 203 College Physics I Fall 2012 S. A. Yost Chapter 3 Motion in 2 Dimensions.

Vectors. Vectors and Direction Vectors are quantities that have a size and a direction. Vectors are quantities that have a size and a direction. A quantity.

Chapter 3 : Vectors - Introduction - Addition of Vectors - Subtraction of Vectors - Scalar Multiplication of Vectors - Components of Vectors - Magnitude.

1.1 – 1.2 The Geometry and Algebra of Vectors.  Quantities that have magnitude but not direction are called scalars. Ex: Area, volume, temperature, time,

Absolute Value Equalities and Inequalities Absolute value: The distance from zero on the number line. Example: The absolute value of 7, written as |7|,

POSITION VECTORS & FORCE VECTORS

Slope – Parallel and Perpendicular Lines Mrs. King and Ms. Reed Geometry Unit 12, Day 9

Vectors in the Plane Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 A ball flies through the air at a certain speed.

H.Melikyan/12001 Vectors Dr.Hayk Melikyan Departmen of Mathematics and CS

Chapter 6 Additional Topics in Trigonometry

Section 10.2a VECTORS IN THE PLANE. Vectors in the Plane Some quantities only have magnitude, and are called scalars … Examples? Some quantities have.

Vectors A quantity which has both magnitude and direction is called a vector. Vector notations A B a AB = a AB x and y are the components of vector AB.

Vectors Definition: A vector quantity is one which has both magnitude and direction One of the simplest vectors is displacement… it has an associated distance.

Vectors Chapter 3, Sections 1 and 2. Vectors and Scalars Measured quantities can be of two types Scalar quantities: only require magnitude (and proper.

General physics I, lec 1 By: T.A.Eleyan 1 Lecture (2)

Vectors Vectors are represented by a directed line segment its length representing the magnitude and an arrow indicating the direction A B or u u This.

Vectors Day 2. Scalar Multiplication A vector can be multiplied by a real number Multiplying a vector by a positive number changes its size, but not its.

Geometric Vectors 8-1. What is a vector? Suppose we are both traveling 65mph on Highway 169 and we pass each other going opposite directions. I’m heading.

Physics for Scientists and Engineers, 6e Chapter 3 - Vectors.

13.4 Vectors. When a boat moves from point A to point B, it’s journey can be represented by drawing an arrow from A to B. AB Read vector AB A B.

HWQ Find the xy trace:.

Honors Pre-Calculus 12.1 Vectors Page 419 Objective: Perform basic operations on vectors.

Analytic Geometry o f Space 3D Space (right-handed coordinate system) Introduction to Vectors –Let –We may to know the displacement from P to Q From P.

8.1 and 8.2 answers. 8.3: Vectors February 9, 2009.

CHAPTER 3: VECTORS NHAA/IMK/UNIMAP.

8.4 Vectors. A vector is a quantity that has both magnitude and direction. Vectors in the plane can be represented by arrows. The length of the arrow.

Vectors in the Plane Objectives: Define a vector What are the basic terms associated with vectors?

Vectors in Two Dimensions. VECTOR REPRESENTATION A vector represents those physical quantities such as velocity that have both a magnitude and a direction.

Copyright © Cengage Learning. All rights reserved. 6.3 Vectors in the Plane.

11.1 Vectors in the Plane.  Quantities that have magnitude but not direction are called scalars. Ex: Area, volume, temperature, time, etc.  Quantities.

STROUD Worked examples and exercises are in the text Programme 6: Vectors VECTORS PROGRAMME 6.

Lesson 82 – Geometric Vectors HL Math - Santowski.

Engineering Fundamentals Session 6 (1.5 hours). Scaler versus Vector Scaler ( 向量 ): : described by magnitude –E.g. length, mass, time, speed, etc Vector(

Section 6.3. A ball flies through the air at a certain speed and in a particular direction. The speed and direction are the velocity of the ball. The.

STROUD Worked examples and exercises are in the text PROGRAMME 6 VECTORS.

Are the quantities that has magnitude only only  Length  Area  Volume  Time  Mass Are quantities that has both magnitude and a direction in space.

Introduction to Vectors Section Vectors are an essential tool in physics and a very significant part of mathematics. Their primary application.

11.5 Vectors in the Plane Do Now A man is at the top of a lighthouse 100 ft high and spots a ship in the ocean. His angle of depression to the ship is.

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.

Vector projections (resolutes)

Outline Addition and subtraction of vectors Vector decomposition

Vectors in the Plane.

Parallel and Perpendicular Lines 4.4.

CHAPTER 13 Geometry and Algebra.

Definition and Notation

Lesson 63 Introduction to Vectors Lesson #1: Vectors are not rays.

Ch. 15- Vectors in 2-D.

Chapter 3 Vectors Questions 3-1 Vectors and Scalars

Vectors Definition: A vector quantity is one which has both magnitude and direction One of the simplest vectors is called a displacement… it has an associated.

Digital Lesson Vectors in the Plane.

6.3 Vectors in the Plane Ref. p. 424.

Vectors in the Plane.

CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.

Presentation transcript:

Vectors Lesson 13.4 Pre-AP Geometry

Lesson Focus This lesson defines the concept of a vector. Vectors have important applications in physics, engineering, and other applied sciences.

Basic Terms Vector A directed quantity that has both magnitude and direction. Magnitude A scalar value having physical units. The magnitude of a mathematical object is its size or absolute value. Direction The spatial relation between something and the course along which it points or moves.

Vector

Vector AB shows the distance and direction from point A to point B. The magnitude of vector AB is the distance from A to B. The magnitude of a vector is like the absolute value of a number. It is never a negative number. The direction to B from A is found by determining the x- component and the y-component of the vector.

Vector Two vectors are equal if they have the same magnitude and the same direction. Two vectors are parallel if they have the same or opposite directions. Two vectors are perpendicular if they have perpendicular directions.

Multiplying by a Scalar Multiplying a vector by a scalar multiplies the magnitude of the vector. If the scalar multiple is negative, then the direction of the vector is reversed.

Vector Sum

Geometer’s Sketchpad Examples 01 Vector Basics 02 Vector Basics 03 Vector Basics 04 Vector Addition 07 Vector Length (Magnitude)

Example #1 Given: P(-3, 4) and Q(-2, -2) Sketch vector PQ, then find the magnitude and direction of vector PQ. Solution: Magnitude: Direction:

Example #2 Given: P(-3, 4) and Q(-2, -2) Find: and Solution:

Example #3 Show that (6, -3) and (-4, 2) are parallel. Solution: The slope of (6, -3) is -1/2. The slope of (-4, 2) is -1/2. The slopes are equal so the vectors are parallel.

Example #4 Show that (6, -3) and (2, 4) are perpendicular. Solution: The slope of (6, -3) is -1/2. The slope of (2, 4) is 2. Since -1/2  2 = -1, the vectors are perpendicular.

Is a vector a ray?

No If B is between A and C, then ray AB and ray AC are the same ray, but vector AB  vector AC. The magnitude of vector AC is greater than the magnitude of vector AB.

Written Exercises Problem Set 13.4A, p.541: # (even)