Dot Product and Orthogonal. Dot product…? Does anyone here know the definition of work? Is it the same as me saying I am standing here working hard? To.

Slides:



Advertisements
Similar presentations
Chapter 10 Vocabulary.
Advertisements

Euclidean m-Space & Linear Equations Euclidean m-space.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 Section 6.7 Dot Product.
The Dot Product (MAT 170) Sections 6.7
The Dot Product Sections 6.7. Objectives Calculate the dot product of two vectors. Calculate the angle between two vectors. Use the dot product to determine.
10.5 The Dot Product. Theorem Properties of Dot Product If u, v, and w are vectors, then Commutative Property Distributive Property.
Section 6.7 The Dot Product. Overview From last section, adding two vectors results in another vector. So also does multiplying a scalar (real number)
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.
UNIT 1 VECTORS. SECTION 1.1 VECTOR CONCEPTS A vector is a mathematical object with both MAGNITUDE (size) and DIRECTION.
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.
Mrs. Rivas International Studies Charter School..
Vectors and the Geometry of Space
6.4 Vectors and Dot Products The Definition of the Dot Product of Two Vectors The dot product of u = and v = is Ex.’s Find each dot product.
The Cross Product Third Type of Multiplying Vectors.
Section 9.4: The Cross Product Practice HW from Stewart Textbook (not to hand in) p. 664 # 1, 7-17.
H.Melikyan/12001 Vectors Dr.Hayk Melikyan Departmen of Mathematics and CS
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.
Angles Between Vectors Orthogonal Vectors
13 B Lines in 2D and 3D. The vector AB and the vector equation of the line AB are very different things. x x x x The line AB is a line passing through.
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 ∙
Dot Products Objectives of this Section Find the Dot Product of Two Vectors Find the Angle Between Two Vectors Determine Whether Two Vectors and Parallel.
6.4 Vectors and Dot Products. Dot Product is a third vector operation. This vector operation yields a scalar (a single number) not another vector. The.
Honors Pre-Calculus 12-4 The Dot Product Page: 441 Objective: To define and apply the dot product.
Warm UpMar. 14 th 1.Find the magnitude and direction of a vector with initial point (-5, 7) and terminal point (-1, -3) 2.Find, in simplest form, the unit.
6.4 VECTORS AND DOT PRODUCTS Copyright © Cengage Learning. All rights reserved.
A rule that combines two vectors to produce a scalar.
Section 12.3 The Dot Product
The Vector Equation of a Line The Angle Between 2 Lines 13C.
Section 11.2 Space Coordinates and Vectors in Space.
Vectors and Dot Product 6.4 JMerrill, Quick Review of Vectors: Definitions Vectors are quantities that are described by direction and magnitude.
1 st Day Section 6.4. Definition of Dot Product The dot product of vector u and vector v is A dot product is always a scalar (real #). Why?
Discrete Math Section 12.4 Define and apply the dot product of vectors Consider the vector equations; (x,y) = (1,4) + t its slope is 3/2 (x,y) = (-2,5)
Today in Precalculus Turn in graded wkst and page 511: 1-8 Notes:
Section 4.2 – The Dot Product. The Dot Product (inner product) where is the angle between the two vectors we refer to the vectors as ORTHOGONAL.
Section 9.3: The Dot Product Practice HW from Stewart Textbook (not to hand in) p. 655 # 3-8, 11, 13-15, 17,
The Dot Product. Note v and w are parallel if there exists a number, n such that v = nw v and w are orthogonal if the angle between them is 90 o.
The definition of the product of two vectors is: 1 This is called the dot product. Notice the answer is just a number NOT a vector.
ME 201 Engineering Mechanics: Statics Chapter 2 – Part E 2.9 Dot Product.
6.4 Vector and Dot Products. Dot Product  This vector product results in a scalar  Example 1: Find the dot product.
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.
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.
11.6 Dot Product and Angle between Vectors Do Now Find the unit vector of 3i + 4j.
Dr. Shildneck. Dot Product Again, there are two types of Vector Multiplication. The inner product,called the Dot Product, and the outer product called.
Chapter 4 Vector Spaces Linear Algebra. Ch04_2 Definition 1. Let be a sequence of n real numbers. The set of all such sequences is called n-space (or.
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.
The Cross Product. We have two ways to multiply two vectors. One way is the scalar or dot product. The other way is called the vector product or cross.
Warm Up 1)Find the magnitude and direction of a vector with initial point (-5, 7) and terminal point (-1, -3). 2)Find, in simplest form, the unit vector.
EXAMPLE FORMULA DEFINITION 1.
Dot Product of Vectors.
Dot Product and Angle Between Two Vectors
Outline Addition and subtraction of vectors Vector decomposition
Lecture 3 0f 8 Topic 5: VECTORS 5.3 Scalar Product.
Vectors and Angles Lesson 10.3b.
4.4 The Dot Product.
6.2 Dot Products of Vectors
Scalars and Vectors.
Law of sines Law of cosines Page 326, Textbook section 6.1
8.5 The Dot Product.
Angles Between Vectors Orthogonal Vectors
Vectors, Linear Combinations and Linear Independence
Section 3.2 – The Dot Product
10.6: Applications of Vectors in the Plane
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Angle between two vectors
6-2 Dot Product of Vectors.
Homework Questions!.
Vectors and Dot Products
RAYAT SHIKSHAN SANSTHA’S S.M.JOSHI COLLEGE HADAPSAR, PUNE
Dots and Cross Products of Vectors in Space
Presentation transcript:

Dot Product and Orthogonal

Dot product…? Does anyone here know the definition of work? Is it the same as me saying I am standing here working hard? To understand what is involved in real work, we turn to a new vector operation called the dot product. The dot product of two vectors result in a scalar (a real number) This is different from the other 2 vector operations you learned (vector addition and scalar multiplication) which their results were vectors.

Dot product

Examples

Deriving an alternate Dot Product Formula (based on the angle between the vectors) u w v

Example:

Parallel Vectors

Orthogonal

The Zero Vector

Homework Page 719 #1-32 ALL

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com Inc. All rights reserved.