According to properties of the dot product, A ( B + C ) equals _________. A) (A B) +( B C) B) (A + B) ( A + C ) C) (A B) – ( A C) D) ( A B ) + ( A C) READING.

Slides:



Advertisements
Similar presentations
What are the x- and y-components of the vector
Advertisements

Fun with Vectors. Definition A vector is a quantity that has both magnitude and direction Examples?
MOMENT OF A COUPLE (Section 4.6)
Problem lb A couple of magnitude 30 lb
APPLICATION OF VECTOR ADDITION
Students will be able to : a) Resolve a 2-D vector into components
Physics 1D03 - Lecture 31 Vectors Scalars and Vectors Vector Components and Arithmetic Vectors in 3 Dimensions Unit vectors i, j, k Serway and Jewett Chapter.
Vector Products (Dot Product). Vector Algebra The Three Products.
ATTENTION QUIZ Forces F1 , F2 and F3 are acting on a particle in static equilibrium. If F1 = {F1X i + 3j – 4k} N, F2 = {– i + F2Y j +
POSITION & FORCE VECTORS (Sections ) Today’s Objectives: Students will be able to : a) Represent a position vector in Cartesian coordinate form,
READING QUIZ A)to move a body towards the point or axis. B)to rotate a body about the point or axis. C)to deform a body. D)to lift a body. The moment of.
1. The unit vector of a force is a vector of A) magnitude 0 in the opposite direction of the force. B) magnitude 0 in the same direction as the force.
READING QUIZ The resultant force of a given couple system is always _______. A) positive B) negative C) zero D) None of the above.
READING QUIZ The moment of a force about a specified axis can be determined using ___. A) a scalar analysis only B) a vector analysis only C) either a.
For any two vectors A and B, which of the following equations is false. A) A – A = 0 B) A – B = A + B C) A + B = B + A D) A/a = 1/a (A), where ‘a’ is a.
1. A unit vector is A) without dimensions. B) without direction. C) without magnitude. D) None of the above. 2. The force F = (3 i + 4 j ) N has a magnitude.
DOT PRODUCT (Section 2.9) Today’s Objective:
Digital Lesson Vectors.
10.5 The Dot Product. Theorem Properties of Dot Product If u, v, and w are vectors, then Commutative Property Distributive Property.
MOMENT ABOUT AN AXIS Today’s Objectives:
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)
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.
POSITION VECTORS & FORCE VECTORS
MOMENT ABOUT AN AXIS In-Class Activities: Check Homework Reading Quiz Applications Scalar Analysis Vector Analysis Concept Quiz Group Problem Solving Attention.
Physics 201 2: Vectors Coordinate systems Vectors and scalars Rules of combination for vectors Unit vectors Components and coordinates Displacement and.
MOMENT ABOUT AN AXIS Today’s Objectives: Students will be able to determine the moment of a force about an axis using a) scalar analysis, and b) vector.
Vectors. Vectors and Direction Vectors are quantities that have a size and a direction. Vectors are quantities that have a size and a direction. A quantity.
POSITION & FORCE VECTORS (Sections ) Today’s Objectives: Students will be able to : a) Represent a position vector in Cartesian coordinate form,
POSITION VECTORS & FORCE VECTORS In-Class Activities: Check Homework Reading Quiz Applications / Relevance Write Position Vectors Write a Force Vector.
POSITION VECTORS & FORCE VECTORS
DOT PRODUCT In-Class Activities: Check Homework Reading Quiz Applications / Relevance Dot product - Definition Angle Determination Determining the Projection.
Non Linear Arrays of charges Contents: 2-D Arrays Example Whiteboards.
Proof Quiz Review 13 Questions…Pay Attention. A postulate is this.
VECTORS (Ch. 12) Vectors in the plane Definition: A vector v in the Cartesian plane is an ordered pair of real numbers:  a,b . We write v =  a,b  and.
Sec 13.3The Dot Product Definition: The dot product is sometimes called the scalar product or the inner product of two vectors.
Calculus III Chapter 12 Br. Joel Baumeyer Christian Brothers University.
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.
Lesson 6.4 – Dot Products The dot product of two vectors is given by
MOMENT OF A COUPLE In-Class activities: Check Homework Reading Quiz Applications Moment of a Couple Concept Quiz Group Problem Solving Attention Quiz Today’s.
Scalar Product (Dot product) of vectors:, are vectors and given like that = (x 1,y 1 ) and = (x 2,y 2 ). We can define the scalar product as:. = = x 1.x.
8.1 and 8.2 answers. 8.3: Vectors February 9, 2009.
THREE-DIMENSIONAL FORCE SYSTEMS In-class Activities: Check Homework Reading Quiz Applications Equations of Equilibrium Concept Questions Group Problem.
Homework Review (Ch. 1 & 2) 1-6 (pg. 15) 1-8 (pg. 15) 2-10 (pg. 28) 2-32 (pg. 39) 2-57 (pg. 42)  Any questions???
MOMENT ABOUT AN AXIS Today’s Objectives: Students will be able to determine the moment of a force about an axis using a) scalar analysis, and b) vector.
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)
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.
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.
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.
Objective: Find the dot product of two vectors. Find the angle between two vectors. Dot product definition Example 1 Find the dot product. v = 2i – j w.
Statics, Fourteenth Edition R.C. Hibbeler Copyright ©2016 by Pearson Education, Inc. All rights reserved. In-Class Activities: Check Homework Reading Quiz.
C H. 6 – A DDITIONAL T OPICS IN T RIGONOMETRY 6.4 – Dot Products.
Dot Product of Vectors.
Sullivan Algebra and Trigonometry: Section 10.5
ES2501: Statics/Unit 4-1: Decomposition of a Force
DOT PRODUCT Today’s Objective:
Outline Addition and subtraction of vectors Vector decomposition
MOMENT ABOUT AN AXIS (Section 4.5)
8.5 The Dot Product.
Chapter 9 Review.
Vectors, Linear Combinations and Linear Independence
Section 3.2 – The Dot Product
DOT PRODUCT Today’s Objective:
Example: If line AB is parallel to line CD and s is parallel to t, find the measure of all the angles when m< 1 = 100°. Justify your answers. t
Vectors and Dot Products
Vectors - Introduction Contents:
Serway and Jewett Chapter 3
Presentation transcript:

According to properties of the dot product, A ( B + C ) equals _________. A) (A B) +( B C) B) (A + B) ( A + C ) C) (A B) – ( A C) D) ( A B ) + ( A C) READING QUIZ

Using the definition of the dot product, the angle  formed between the tails of vectors A and B is A)  = cos -1 ( AB ) B)  = cos -1 ( AB ) C)  = sin -1 ( A B ) D)  = sin -1 ( AB ) AB READING QUIZ

CONCEPT QUIZ The projection of force F along a line can be determined by taking the dot product of F with A) the position vector of the two point on the line. B) the unit vector along the force. C) the unit vector along the line. D) None of the above.

CONCEPT QUIZ The dot product of two force vectors parallel to each other is __. A) 1 B) 0 C) –1 D) Can not be determined due to lack of information.

ATTENTION QUIZ Select the false statement. A) i i = 1 B) i j = 0 C) j k = 0 D) k i = -1

ATTENTION QUIZ The dot product of F = {4 i + j } N with the vector – i m is A) 4 N - m B) 1 N - m C) 0 N - m D) - 4 N - m