A#40 Vectors Day 6 Paper #1 Review.

Slides:

Advertisements

Similar presentations

Vectors in 2 and 3 dimensions

Advertisements

Addition of vectors (i) Triangle Rule [For vectors with a common point] C B A.

Addition of vectors (i) Triangle Rule [For vectors with a common point] C B A.

Exam 1, Fall 2014 CE 2200.

©thevisualclassroom.com Medians and Perpendicular bisectors: 2.10 Using Point of Intersection to Solve Problems Centroid: Intersection of the medians of.

DOT PRODUCT (Section 2.9) Today’s Objective:

ENGR 215 ~ Dynamics Sections Relative Motion Analysis.

EGR 280 Mechanics 9 – Particle Kinematics II. Curvilinear motion of particles Let the vector from the origin of a fixed coordinate system to the particle.

Chapter 14 Section 14.3 Curves. x y z To get the equation of the line we need to know two things, a direction vector d and a point on the line P. To find.

Physics 203 – College Physics I Department of Physics – The Citadel Physics 203 College Physics I Fall 2012 S. A. Yost Chapter 3 Motion in 2 Dimensions.

Higher Maths Revision Notes Vectors Get Started. Vectors in three dimensions use scalar product to find the angle between two directed line segments know.

Chapter 7 Section 1.  Students will write ratios and solve proportions.

Vectors and Vector Multiplication. Vector quantities are those that have magnitude and direction, such as: Displacement,  x or Velocity, Acceleration,

Vectors Precalculus. Vectors A vector is an object that has a magnitude and a direction. Given two points P: & Q: on the plane, a vector v that connects.

Circle : A closed curve formed in such a way that any point on this curve is equidistant from a fixed point which is in the interior of the curve. A D.

Dilations Shape and Space. 6.7 cm 5.8 cm ? ? Find the missing lengths The second picture is an enlargement of the first picture. What are the missing.

Vectors Vectors are represented by a directed line segment its length representing the magnitude and an arrow indicating the direction A B or u u This.

Teach A Level Maths Vectors for Mechanics. Volume 4: Mechanics 1 Vectors for Mechanics.

Physics. Session Kinematics - 1 Session Opener You fly from Delhi to Mumbai New Delhi Mumbai Hyderabad Then you fly from Mumbai to Hyderabad Does it.

RELATIVE MOTION ANALYSIS: VELOCITY

المحاضرة الخامسة. 4.1 The Position, Velocity, and Acceleration Vectors The position of a particle by its position vector r, drawn from the origin of some.

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

Vectors Lesson 13.4 Pre-AP Geometry. Lesson Focus This lesson defines the concept of a vector. Vectors have important applications in physics, engineering,

Unit 2 Test Review Geometry WED 1/22/2014. Pre-Assessment Answer the question on your own paper.

(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition.

Lesson 82 – Geometric Vectors HL Math - Santowski.

8.4 Proportionality Theorems. Geogebra Investigation 1)Draw a triangle ABC. 2)Place point D on side AB. 3)Draw a line through point D parallel to BC.

Vectors Vectors and Scalars Properties of vectors Adding / Sub of vectors Multiplication by a Scalar Position Vector Collinearity Section Formula.

Warm up: Draw a vector on the Cartesian coordinate plane, and describe this vector in words.

Geometry is the branch of mathematics which deals with the properties and relations of line, angles, surfaces and solids. The word geometry is divided.

SCALARS & VECTORS. Physical Quantities All those quantities which can be measured are called physical quantities. Physical Quantities can be measured.

12-2 MATRIX MULTIPLICATION MULTIPLY MATRICES BY USING SCALAR AND MATRIX MULTIPLICATION.

12 A VECTORS AND SCALARS 12 B GEOMETRIC OPERATIONS HOMEWORK: VIEW POWER POINT BEFORE NEXT CLASS.

Vectors and Scalars. Adding Vectors A B A+B A B Find B-A = -A + B A B -A-A B -A-A -A+B-A+B B-A =B-A A+(B-A)=B.

CHAPTER - 8 MOTION CLASS :- IX MADE BY :- MANAS MAHAJAN SCHOOL :- K.V. GANESHKHIND PUNE-7.

Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

Vector projections (resolutes)

Drawing a sketch is always worth the time and effort involved

Eugene, Yelim, Victoria and Matt

Vectors in the Plane Section 10.2.

3D Coordinates In the real world points in space can be located using a 3D coordinate system. For example, air traffic controllers find the location a.

REVIEW PROBLEMS FOR TEST 1 PART 3

Vectors and Scalars.

تصنيف التفاعلات الكيميائية

t Circles – Tangent Lines

Motion Along a Line: Vectors

CHAPTER 13 Geometry and Algebra.

Definition and Notation

Lesson 78 – Geometric Vectors

DO NOW Directions (Part 1):

Amardeep & Nirmal ,Dept of Aero, Mvjce

Line, line segment and rays.

Vectors and Scalars.

Tuesday, December 04, 2018 Geometry Revision!.

Vectors Vectors are a way to describe motion that is not in a straight line. All measurements can be put into two categories: Scalars = magnitude Vectors.

Module 15: Lesson 4 Perpendicular Bisectors of Triangles

Jeopardy Slopes and Lines Exponents Radicals $100 $ $100 $100

Ch. 15- Vectors in 2-D.

Solving Linear Equations

MATH 1330 Final Exam Review 1.

Higher Maths The Straight Line Strategies Click to start

Vectors and Scalars.

Vector Equations Trig 6.12 Obj: Find the vector equation parallel to a given vector and through a given point.

CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.

Parallel Forces and Couples

KINEMATICS OF MACHINERY

Presentation transcript:

A#40 Vectors Day 6 Paper #1 Review

A#40 day 6 Vectors paper1

N2008/SP1/TZ0

V e c t o r s N2008/SP1/TZ0 (i) AO +OB = – a + b = b – a Recall: OB = b OA = a AO = -a (ii) speed = Recall: Speed is the magnitude of the velocity vector. Particle motion

V e c t o r s N2008/SP1/TZ0 (b) Equation of line L: or Particle motion

2008/SP1/TZ2 Section B Consider the points A(1, 5, 4), B(3, 1, 2) and D(3, k, 2) with (AD) perpendicular to (AB).

Perpendicular vectors: Scalar product is 0 2008/SP1/TZ2 Section B (i) AB = AO +OB = – a + b = b – a (ii) AD = AO +OD = – a + d = d – a Perpendicular vectors: Scalar product is 0

Perpendicular vectors: Scalar product is 0 2008/SP1/TZ2 Section B (b) 4 – 4(k – 5) + 4 = 0 4k + 28 = 0 k = 7 (c) Recall: a | b => Scalar product = 0 Perpendicular vectors: Scalar product is 0

Method 2: The scalar product of | vectors is 0 2008/SP1/TZ2 Section B V e c t o r s (c) (cont) OC = OB +BC = b + BC (d) Given AD | AB, since BC = (½)AD, BC has the same direction as AD. So BC | AB and ABC = 90o. cos ABC = cos 90o = 0. ^ A D C B ^ Method 2: The scalar product of | vectors is 0

2010/SP1/TZ2 2010/SP1/TZ2

The unit vector has magnitude of 1 2010/SP1/TZ2 V e c t o r s BC = BA +AC = AC – AB (b) Length (magnitude) of AB = Unit vector is: The unit vector has magnitude of 1

The scalar product of | vectors is 0 2010/SP1/TZ2 (c) => AB | AC. Alternately, cos  = 0 Vectors perpendicular AB | AC The scalar product of | vectors is 0

N09/5/MATME/SP1/ENG/TZ0/ N09/5/MATME/SP1/ENG/TZ0/

N09/5/MATME/SP1/ENG/TZ0/ N09/5/MATME/SP1/ENG/TZ0/

2010/SP1/TZ1/Section B

Parallel vectors are scalar multiples of one another 2010/SP1/TZ1/Section B (a) Equations of parallel lines: Parallel vectors are scalar multiples of one another

The scalar product of | vectors is 0 2010/SP1/TZ1/Section B (b) Equations of perpendicular lines: (2)(-7) + (1)(-2) + (-8)(k) = –14 – 2 – 8k = 0 – 16 – 8k = 0 k = – 2 The scalar product of | vectors is 0

V e c t o r s 2010/SP1/TZ1/Section B (c) L1 and L3 intersect at A. Set L1 = L3. Solve. (-3) + p(2) = (5) + q(-7) (-1) + p(1) = (0) + q(-2) p + 2q = 1 (-25) + p(-8) = (3) + q(-2) - (-8p + 2q) = -(28) 9p = -27 => p = -3 q = 2 Point A is (-9, -4, -1) Intersecting lines

Position vectors OA and OB. 2010/SP1/TZ1/Section B V e c t o r s (d) (i) AO +OB = – a + b = b – a Recall: OB = b OA = a AO = -a Position vectors OA and OB.

2010/SP1/TZ1/Section B V e c t o r s (d) (ii) AC = AB +BC (ii) magnitude = Particle motion