6.2 Dot Product of Vectors.

Slides:



Advertisements
Similar presentations
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 Section 6.7 Dot Product.
Advertisements

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.
Phy 212: General Physics II Chapter : Topic Lecture Notes.
Copyright © 2011 Pearson, Inc. 6.2 Dot Product of Vectors.
11.3 The Dot Product of Two Vectors. 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.
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.
Copyright © Cengage Learning. All rights reserved. 6.4 Vectors and Dot Products.
Kinetic energy Vector dot product (scalar product) Definition of work done by a force on an object Work-kinetic-energy theorem Lecture 10: Work and kinetic.
6.4 Vectors and Dot Products
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.
Chapter 5: The Orthogonality and Least Squares
Dot Product of Vectors. Quick Review Quick Review Solutions.
Applications of Trigonometry
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1 Homework, Page
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1.
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
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 Product TS: Developing a capacity for working within ambiguity Warm Up: Copy the below into your notebook The dot product of u = and v = is given by.
Dot Product Second Type of Product Using Vectors.
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.
Dot ProductOperations with Dot Products Angle Between Two Vectors Parallel, Orthogonal, or Neither
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.
Lesson 6.4 – Dot Products The dot product of two vectors is given by
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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1 What you’ll learn about Two-Dimensional Vectors Vector Operations.
Section 12.3 The Dot Product
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.
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 Another.
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.
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.
Chapter 4 Vector Spaces Linear Algebra. Ch04_2 Definition 1: ……………………………………………………………………. The elements in R n called …………. 4.1 The vector Space R n Addition.
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.
11.3 The Cross Product of Two Vectors. Cross product A vector in space that is orthogonal to two given vectors If u=u 1 i+u 2 j+u 3 k and v=v 1 i+v 2.
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.
Dot Product So far, we haven’t talked about how to multiply two vectors…because there are two ways to “multiply” them. Def. Let and, then the dot product.
11.6 Dot Product and Angle between Vectors Do Now Find the unit vector of 3i + 4j.
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.
Vectors – The Dot Product Lecture 12 Mon, Sep 22, 2003.
CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.
Dot Product of Vectors.
Dot Product of Vectors.
Dot Product and Angle Between Two Vectors
Sullivan Algebra and Trigonometry: Section 10.5
6.2 - Dot Product of Vectors
Vectors and Angles Lesson 10.3b.
4.4 The Dot Product.
6.2 Dot Products of Vectors
Law of sines Law of cosines Page 326, Textbook section 6.1
8.5 The Dot Product.
6.2 Dot Product of Vectors.
Scalar and Vector Projections
Cross Products Lecture 19 Fri, Oct 21, 2005.
Section 3.2 – The Dot Product
Find {image} , if {image} and {image} .
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Mathematics.
Homework Questions!.
Find {image} , if {image} and {image} .
36. Dot Product of Vectors.
25. Dot Product of Vectors.
Vectors and Dot Products
Presentation transcript:

6.2 Dot Product of Vectors

What you’ll learn about The Dot Product Angle Between Vectors Projecting One Vector onto Another Work … and why Vectors are used extensively in mathematics and science applications such as determining the net effect of several forces acting on an object and computing the work done by a force acting on an object.

Dot Product

Properties of the Dot Product Let u, v, and w be vectors and let c be a scalar. 1. u·v = v·u 2. u·u = |u|2 3. 0·u = 0 4. u·(v + w) = u·v + u·w (u + v) ·w = u·w + v·w 5. (cu)·v = u·(cv) = c(u·v)

Example Finding the Dot Product

Example Finding the Dot Product

Angle Between Two Vectors

Example Finding the Angle Between Vectors

Example Finding the Angle Between Vectors

Orthogonal Vectors The vectors u and v are orthogonal if and only if u·v = 0.

Projection of u and v

Work

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

© 2025 SlidePlayer.com. Inc. All rights reserved.