Objective: Find the dot product of two vectors. Find the angle between two vectors. Dot product definition Example 1 Find the dot product. v = 2i – j w.

Slides:

Advertisements

Similar presentations

What are the x- and y-components of the vector

Advertisements

Fun with Vectors. Definition A vector is a quantity that has both magnitude and direction Examples?

b a The Vector or x Product

Vectors Lesson 4.3.

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.

Vector Products (Dot Product). Vector Algebra The Three Products.

READING QUIZ The resultant force of a given couple system is always _______. A) positive B) negative C) zero D) None of the above.

For any two vectors A and B, which of the following equations is false. A) A – A = 0 B) A – B = A + B C) A + B = B + A D) A/a = 1/a (A), where ‘a’ is a.

1. A unit vector is A) without dimensions. B) without direction. C) without magnitude. D) None of the above. 2. The force F = (3 i + 4 j ) N has a magnitude.

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.

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

VECTORS in 3-D Space Vector Decomposition Addition of Vectors:

Chapter 12 – Vectors and the Geometry of Space

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.

According to properties of the dot product, A ( B + C ) equals _________. A) (A B) +( B C) B) (A + B) ( A + C ) C) (A B) – ( A C) D) ( A B ) + ( A C) READING.

24. Dot Product of Vectors. What you’ll learn about  How to find the Dot Product  How to find the Angle Between Vectors  Projecting One Vector onto.

6.4 Vectors and Dot Products

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

12.9 Parallel & Perpendicular Vectors in Two Dimensions

Assigned work: pg.407 #1-13 Recall dot product produces a scalar from two vectors. Today we examine a Cross Product (or Vector Product) which produces.

Applications of Vectors. Definition: Resultant: The result of two vectors acting on a point at the same time. Equilibrant: The opposite vector of the.

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

Introduction to Vectors

Aim: How can we use the parallelogram method of adding vectors? Do Now: Find the resultant of the following vectors through graphical means: 90 m/s South.

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.

Chapter 6 Additional Topics in Trigonometry. Copyright © Houghton Mifflin Company. All rights reserved. Digital Figures, 6–2 Section 6.1, Law of Sines,

Sec 13.3The Dot Product Definition: The dot product is sometimes called the scalar product or the inner product of two vectors.

Assigned work: pg.398 #1,3,7,8,11-14 pg. 419 #3 (work) Recall: Dot Product.

A rule that combines two vectors to produce a scalar.

Vectors Vectors vs. Scalars Vector Addition Vector Components

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

A.) Scalar - A single number which is used to represent a quantity indicating magnitude or size. B.) Vector - A representation of certain quantities which.

8.5 The Dot Product Precalculus. Definition of the Dot Product If u= and v= are vectors, then their dot product (u v) is defined by: u v = a 1 a 2 + b.

Statics (ENGR 2214) Prof. S. Nasseri Statics ENGR 2214 Vectors in three dimensional space.

Warm up:. Problem: What is the angle between the vectors (1,2) and (-1, 3)?

12.3 The Dot Product. The dot product of u and v in the plane is The dot product of u and v in space is Two vectors u and v are orthogonal  if they meet.

Mr. Rommel South Salem HS Vectors Parallel and Perpendicular Vectors Dot Product.

6.4 Vectors and Dot Products Objectives: Students will find the dot product of two vectors and use properties of the dot product. Students will find angles.

We will use the distance formula and the law of cosines to develop a formula to find the angle between two vectors.

11. Section 12.1 Vectors Vectors What is a vector and how do you combine them?

Homework Questions. Chapter 6 Section 6.1 Vectors.

CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.

Lesson 12 – 7 Geometric Vectors

Dot Product of Vectors.

Section 6.2: Dot Product of Vectors

ES2501: Statics/Unit 4-1: Decomposition of a Force

Expressing a Vector in 3-D Space

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

Law of sines Law of cosines Page 326, Textbook section 6.1

Angles Between Vectors Orthogonal Vectors

Multiplying Vectors - Dot and Cross Products -

How to calculate a dot product

Vectors, Linear Combinations and Linear Independence

Physics 133 Electromagnetism

Only some of this is review.

Electrostatic force due to spherical shell of charge

Forces in Two Dimensions

Cartesian Vectors In right-handed Cartesian coordinated system, the right thumb points in the positive z direction when the right hand figures are curled.

Cartesian Vectors In right-handed Cartesian coordinated system, the right thumb points in the positive z direction when the right hand figures are curled.

6.1 Vectors in the Plane.

Force Systems Force: Action of one body on another. Effects of a force

Section 6.1: Vectors in a Plane

Electrostatic force due to spherical shell of charge

Methods of Finding Vector Sum

Distinguish between scalars & vectors Add and subtract vectors

DG34 (LAST ONE!)---10 minutes

Scalar and vector quantities

Phys 13 General Physics 1 Vector Product MARLON FLORES SACEDON.

Vectors Lesson 4.3.

Presentation transcript:

Objective: Find the dot product of two vectors. Find the angle between two vectors. Dot product definition Example 1 Find the dot product. v = 2i – j w = 3i – 5j a. b.

Angle between two given vectors

Reminder: Law of Cosine

Example 2 Find the angle between the vectors. a. b.

Assignment Quiz corrections. Pg 719 # 3, 9-13, 17-22

6.6 topics Prove two vectors are equivalent given their endpoints. Find the vector components given the endpoints. Find the vector components given the magnitude and direction angle. Find unit vector in the same direction of given vector. Sketch vector given its components. Find resultant force vector and its magnitude. Find resultant force vector and its direction angle.