The Cross Product.

Slides:

Advertisements

Similar presentations

11.4 The Cross product For an animation of this topic visit:

Advertisements

Geometry of R2 and R3 Dot and Cross Products.

General Physics (PHYS101)

Vector Refresher Part 4 Vector Cross Product Definition Vector Cross Product Definition Right Hand Rule Right Hand Rule Cross Product Calculation Cross.

10.4 Cross product: a vector orthogonal to two given vectors Cross product of two vectors in space (area of parallelogram) Triple Scalar product (volume.

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.

Vector Products (Cross Product). Torque F r T F r T F1F1 F2F2.

Analytic Geometry in Three Dimensions

7/6/2015 Orthogonal Functions Chapter /6/2015 Orthogonal Functions Chapter 7 2.

Example: Determine the angle between the vectors A and B.

1-1 Engineering Electromagnetics Chapter 1: Vector Analysis.

The Cross Product of 2 Vectors 11.3 JMerrill, 2010.

VAVLPVCTYMAUS PSABLADDERZSB EBSANTESHTICL RLDUDSKTTVSRA EDEARCENEAUOD CRFNORSASINTD TPEUUOCPTDATP UNRTMTRBEEXME MIEUSUULSNSNN USNMEMNISAIIT AESXSVPENNISI.

ARCH 689 Parametric Modeling in Architecture Vector Mathematics: Applications Wei Yan, Ph.D. Associate Professor Department of Architecture Texas A&M University.

APPLICATIONS OF TRIGONOMETRY

The Cross Product of Two Vectors In Space Section

Chapter 13 Section 13.5 Lines. x y z A direction vector d for the line can be found by finding the vector from the first point to the second. To get.

The Cross Product Third Type of Multiplying Vectors.

Section 13.4 The Cross Product.

MAT 1236 Calculus III Section 12.5 Part II Equations of Line and Planes

Cross Product of Two Vectors

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

Vectors in 2-Space and 3-Space II

Functions of several variables. Function, Domain and Range.

QPLNHTURBIOTS CADAIASOINCOS OSTPOSTLGVAGT AJRLFKLEROUEA CLARITYSOLSTB HTEAMVSRUVAHI INTERACTPELEL NAPKSOCIALIRI GSOCIOGRAMTST CONFORMITYYTY 14 WORDS ANSWERS.

Words may be in any direction: Horizontal, diagonal, vertical, reverse.

Elementary Linear Algebra Howard Anton Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved. Chapter 3.

Special Parallelograms. Theorem 6-9 Each diagonal of a rhombus bisects the opposite angles it connects.

Review Lecture. The following topics would be covered in the finale exam 1.Lines in the plane 2.The second order curves  Ellipse  Hyperbola  Parabola.

Vector Products (Cross Product). Torque F r T.

Copyright © Cengage Learning. All rights reserved.

1. Determine vectors and scalars from these following quantities: weight, specific heat, density, volume, speed, calories, momentum, energy, distance.

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

Vectors in Space. 1. Describe the set of points (x, y, z) defined by the equation (Similar to p.364 #7-14)

W.A.L.T: Reading and Writing Co-ordinates. Our Aim To locate things using co-ordinate grids

Vector Products.

Mathematics. Session Vectors -2 Session Objectives  Vector (or Cross) Product  Geometrical Representation  Properties of Vector Product  Vector Product.

Composite 3D Transformations. Example of Composite 3D Transformations Try to transform the line segments P 1 P 2 and P 1 P 3 from their start position.

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.

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.

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.

Discrete Math Section 12.9 Define and apply the cross product The cross product of two vectors results in another vector. If v 1 = and v 2 =, the cross.

Dr. Shildneck. Dot Product Again, there are two types of Vector Multiplication. The inner product,called the Dot Product, and the outer product called.

Math /7.5 – Vectors 1. Suppose a car is heading NE (northeast) at 60 mph. We can use a vector to help draw a picture (see right). 2.

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.

6-7 Polygons in the Coordinate Plane. Classifying Quadrilaterals Given the coordinates of the vertices, how would you determine if the quadrilateral is…

CSE 681 Brief Review: Vectors. CSE 681 Vectors Direction in space Normalizing a vector => unit vector Dot product Cross product Parametric form of a line.

Dot Product and Cross Product. Dot Product  Definition:  If a = and b =, then the dot product of a and b is number a · b given by a · b = a 1 b 1 +

The Vector Cross Product

Section 3.4 Cross Product.

Elementary Linear Algebra

Department of Architecture

Outline Addition and subtraction of vectors Vector decomposition

Prime Time Investigation 4 Review

عناصر المثلثات المتشابهة Parts of Similar Triangles

Introduction to Functions

Cross SECTIONS.

Section 3.2 – The Dot Product

2.2 Operations on Algebraic Vectors

Vector Products (Cross Product)

Inverse Functions Part 2

Area of Rectangles and Parallelograms

Dilations Objective:.

Bell work Algebra 2 1. Find ( f ⋅ g)(x) for f(x) =

Similarities Differences

NOTES: 8–5 Applications of Vectors

Warm-Up Solve each proportion. 1) 2)

Presentation transcript:

The Cross Product

1. Find the value of each determinant (Similar to p.370 #7-10)

2. Find the value of each determinant (Similar to p.370 #11-14)

3. Find (a) v x w, (b) w x v, (c) w x w, and (d) v x v (Similar to p

4. Find (a) v x w, (b) w x v, (c) w x w, and (d) v x v (Similar to p

5. Use the given vectors u, v, and w to find each expression 5. Use the given vectors u, v, and w to find each expression. u = 3i – j + 2k v = 4i + j – 5k w = i + j + k (Similar to p.370 #23-40)

6. Use the given vectors u, v, and w to find each expression 6. Use the given vectors u, v, and w to find each expression. u = 3i – j + 2k v = 4i + j – 5k w = i + j + k (Similar to p.370 #23-40)

7. Use the given vectors u, v, and w to find each expression 7. Use the given vectors u, v, and w to find each expression. u = 3i – j + 2k v = 4i + j – 5k w = i + j + k (Similar to p.370 #23-40)

8. Use the given vectors u, v, and w to find each expression 8. Use the given vectors u, v, and w to find each expression. u = 3i – j + 2k v = 4i + j – 5k w = i + j + k (Similar to p.370 #23-40)

9. Use the given vectors u, v, and w to find each expression 9. Use the given vectors u, v, and w to find each expression. u = 3i – j + 2k v = 4i + j – 5k w = i + j + k (Similar to p.370 #41-44) vector orthogonal to both u and v (Hint u x v is orthogonal to both)

11. Find the area of the parallelogram with vertices P1, P2, P3, and P4 (Similar to p.370 #49-52)