Application of Vector product

Slides:

Advertisements

Similar presentations

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

Advertisements

14 Vectors in Three-dimensional Space Case Study

Geometry of R2 and R3 Dot and Cross Products.

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.

Chapter 12 – Vectors and the Geometry of Space 12.4 The Cross Product 1.

The Right Hand Rule b a axb.

The Vector or Cross Product Lecture V1.3 Example 5 Moodle.

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

Lecture 13 Today Basic Laws of Vector Algebra Scalars: e.g. 2 gallons, $1,000, 35ºC Vectors: e.g. velocity: 35mph heading south 3N force toward.

Analytic Geometry in Three Dimensions

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.

Vectors. We will start with a basic review of vectors.

Vector Product Results in a vector.

The Cross Product of 2 Vectors 11.3 JMerrill, 2010.

11 Analytic Geometry in Three Dimensions

The Cross Product of Two Vectors In Space Section

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.

Vectors and the Geometry of Space Copyright © Cengage Learning. All rights reserved.

1 Physics 111/121 Mini-Review Notes on Vectors. 2 Right hand rule: - curl fingers from x to y - thumb points along +z.

Section 13.4 The Cross Product.

MAT 1236 Calculus III Section 12.4 The Cross Product

Torque The magnitude of the torque depends on two things: The distance from the axis of the bolt to the point where the force is applied. This is |r|,

The Sine Law (animated). Sine Law Let’s begin with the triangle  ABC:

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

6.3 Cramer’s Rule and Geometric Interpretations of a Determinant

Vectors and the Geometry of Space 11 Copyright © Cengage Learning. All rights reserved.

Vectors in 2-Space and 3-Space II

Functions of several variables. Function, Domain and Range.

Section 13.4 The Cross Product. Torque Torque is a measure of how much a force acting on an object causes that object to rotate –The object rotates around.

Properties of Vector Operations: u, v, w are vectors. a, b are scalars. 0 is the zero vector. 0 is a scalar zero. 1. u + v = v + u 2. (u + v) + w = u +

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.

Section 11.4 The Cross Product Calculus III September 22, 2009 Berkley High School.

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.

DOT PRODUCT CROSS PRODUCT APPLICATIONS

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

Copyright © Cengage Learning. All rights reserved. 11 Analytic Geometry in Three Dimensions.

Have the following out on your table to show me Exercise A page 83 All 6 questions Blue worksheet of past parametric exam qu’s (3qu) If you don’t have.

Specialist Mathematics Vectors and Geometry Week 3.

Force is a Vector A Force consists of: Magnitude Direction –Line of Action –Sense Point of application –For a particle, all forces act at the same point.

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.

GCSE Mathematics Problem Solving Shape and Measure Higher Tier.

The Cross Product: Objectives

The Sine Rule The Sine Rule is used for cases in which the Cosine Rule cannot be applied. It is used to find: 1. An unknown side, when we are given two.

Section 3.4 Cross Product.

Approximate Running Time is 29 Minutes

Engineering Mechanics Electrical Engineering Department Engr. Abdul Qadir channa.

Math 200 Week 2 - Monday Cross Product.

By the end of Week 2: You would learn how to plot equations in 2 variables in 3-space and how to describe and manipulate with vectors. These are just.

Vectors in The R2 and R3 Sub Chapter : Terminology

The formula for calculating the area of a parallelogram

Cross Products Lecture 19 Fri, Oct 21, 2005.

Lesson 81: The Cross Product of Vectors

2.2 Operations on Algebraic Vectors

Vector Products (Cross Product)

Vectors and the Geometry

Warm-Up #30 Thursday, 5/5 Find the area of the shaded region.

Angle between two vectors

The General Triangle C B A.

Vectors in The R2 and R3 Sub Chapter : Terminology

11 Vectors and the Geometry of Space

The Sine Rule The Sine Rule is used for cases in which the Cosine Rule cannot be applied. It is used to find: 1. An unknown side, when we are given two.

The General Triangle C B A.

Area: Area of a triangle

The Sine Rule The Sine Rule is used for cases in which the Cosine Rule cannot be applied. It is used to find: 1. An unknown side, when we are given two.

Accel Precalc Unit 8: Extended Trigonometry

Find the cross product {image} . {image} .

Presentation transcript:

Application of Vector product

Area of a triangle?

Example-1 Find the area of triangle ABC given A(-1,2,3), B(2,1,4) and C(0,5,-1)

Area of Parallelogram

Example-2 Calculate the area of parallelogram ABCD for A(-1, 2, 2), B(2, -1, 4) and C(0,1,0)

Volume of Parallelepiped

Triple Scalar Product a.(bxc) is known as triple scalar product.

Example-3: Let a = 2i+3j-k, b= 6i-3j+2k and c= 4i+3j-k, Find the Triple Scalar Product. (?????)

Example-4 Verify that the vector a = i+j+k is perpendicular to the cross product aXb where b = 2i-3j+k.

Question of the day!!!!!! Example-5 By making use of the vector product, derive the sine rule. Recall that Sine Rule: