Homework Questions!.

Slides:

Advertisements

Similar presentations

Chapter 6 Vocabulary.

Advertisements

Dot Product ES: Developing a capacity for working within ambiguity Warm Up: Look over the below properties The dot product of u = and v =

Geometry of R2 and R3 Dot and Cross Products.

Euclidean m-Space & Linear Equations Euclidean m-space.

6 6.1 © 2012 Pearson Education, Inc. Orthogonality and Least Squares INNER PRODUCT, LENGTH, AND ORTHOGONALITY.

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.

6 6.1 © 2012 Pearson Education, Inc. Orthogonality and Least Squares INNER PRODUCT, LENGTH, AND ORTHOGONALITY.

Copyright © 2011 Pearson, Inc. 6.2 Dot Product of Vectors.

6.3 Vector in the Plane Magnitude Component form Unit Vector.

Copyright © Cengage Learning. All rights reserved. 6.4 Vectors and Dot Products.

6.4 Vectors and Dot Products

APPLICATIONS OF TRIGONOMETRY

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.

Section 9.4: The Cross Product Practice HW from Stewart Textbook (not to hand in) p. 664 # 1, 7-17.

Dot Product of Vectors. Quick Review Quick Review Solutions.

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

Angles Between Vectors Orthogonal Vectors

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.

Inner Products, Length, and Orthogonality (11/30/05) If v and w are vectors in R n, then their inner (or dot) product is: v  w = v T w That is, you multiply.

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 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.

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.

4.7 – Square Roots and The Pythagorean Theorem Day 2.

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1 What you’ll learn about Two-Dimensional Vectors Vector Operations.

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.

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 3.3 Dot Product; Projections. THE DOT PRODUCT If u and v are vectors in 2- or 3-space and θ is the angle between u and v, then the dot product.

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.

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.

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.

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.

Homework Questions. Chapter 6 Section 6.1 Vectors.

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

Section 6.2: Dot Product of Vectors

Section 3.4 Cross Product.

6.2 - Dot Product of Vectors

6.2 Dot Product of Vectors.

Lecture 3 0f 8 Topic 5: VECTORS 5.3 Scalar 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.

Angles Between Vectors Orthogonal Vectors

Dot Products and projections

Scalar and Vector Projections

Cross Products Lecture 19 Fri, Oct 21, 2005.

Section 11.2 The Quadratic Formula.

Section 3.2 – The Dot Product

10.6: Applications of Vectors in the Plane

Linear Algebra Lecture 38.

Vectors and Dot Products

RAYAT SHIKSHAN SANSTHA’S S.M.JOSHI COLLEGE HADAPSAR, PUNE

Presentation transcript:

Homework Questions!

Section 6.2 Dot Product of Vectors

The dot product (inner product) of U= <U1,U2> and V=<V1,V2> is U · V = U1V1 + U2V2

Properties of 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 1 Find each dot product A. <3, 4> · <5, 2> B. <1, -2> · <-4, 3> C. (2i-j) · (3i-5j)

Example 2: Using dot product to find length Property 2…u · u= |u|2 (Square root both sides) Use the dot product to find the length of the vector u = <4, -3> Use the dot product to find the length of the vector u = <5, -12>

Angle Between Vectors cos Ө = Ө =

Example 3: Finding the angle between vectors Find the angle between the vectors u and v. u = <2, 3> and v = <-2, 5> u = <2, 1> and v = <-1, -3>

Orthogonal Vectors The vectors u and v are orthogonal if and only if u · v = 0. Prove u and v are orthogonal. u = <2, 3> and v = <-6, 4>

Homework p. 519 (1-24)