VECTORSVECTORS Describing paths. VECTOR: line segment with… i. Direction(an angle) ii. Magnitude||v|| = length of vector (distance)

Slides:

Advertisements

Similar presentations

10.2 Vectors and Vector Value Functions

Advertisements

Chapter 10 Vocabulary.

Year 10 Pathway C Mr. D. Patterson.  Distinguish between scalar and vector quantities  Add and subtract vectors in 2 dimensions using scaled diagrams.

Vectors INTRODUCTION SCALAR QUANTITIES: _______________________________________________________ VECTOR QUANTITIES: ________________________________________________________.

8-7 Vectors You used trigonometry to find side lengths and angle measures of right triangles. Perform vector operations geometrically. Perform vector operations.

10.2 day 1: Vectors in the Plane Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 Mesa Verde National Park, Colorado.

10.4 MINIMAL PATH PROBLEMS 10.5 MAXIMUM AND MINIMUM PROBLEMS IN MOTION AND ELSEWHERE.

8-7 Vectors You used trigonometry to find side lengths and angle measures of right triangles. Perform vector operations geometrically. Perform vector operations.

8-6 Vectors Holt McDougal Geometry Holt Geometry.

Vectors Vector: a quantity that has both magnitude (size) and direction Examples: displacement, velocity, acceleration Scalar: a quantity that has no.

1.1 – 1.2 The Geometry and Algebra of Vectors.  Quantities that have magnitude but not direction are called scalars. Ex: Area, volume, temperature, time,

Geometry Vectors CONFIDENTIAL.

8-6 Vectors Warm Up Lesson Presentation Lesson Quiz Holt Geometry.

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.

Vectors TS: Explicitly assessing information and drawing conclusions. Warm Up: a)What are the coordinates of A and B b)What is the distance between A and.

10.2 Vectors and Vector Value Functions. Quantities that we measure that have magnitude but not direction are called scalars. Quantities such as force,

Chapter 3 Vectors. Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the.

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

6.3 Vectors in the Plane I. Vectors. A) Vector = a segment that has both length and direction. 1) Symbol = AB or a bold lower case letter v. 2) Draw a.

Geometry 7.4 Vectors. Vectors A vector is a quantity that has both direction and magnitude (size). Represented with a arrow drawn between two points.

Chapter 3 Vectors. Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the.

Geometric Vectors 8-1. What is a vector? Suppose we are both traveling 65mph on Highway 169 and we pass each other going opposite directions. I’m heading.

Aim: How can we distinguish between a vector and scalar quantity? Do Now: What is the distance from A to B? Describe how a helicopter would know how to.

8-6 Vectors Warm Up Lesson Presentation Lesson Quiz

Vectors 9.7 Chapter 9 Right Triangles and Trigonometry Section 9.7 Vectors Find the magnitude and the direction of a vector. Add vectors.

VectorsVectors. What is a vector quantity? Vectors Vectors are quantities that possess magnitude and direction. »Force »Velocity »Acceleration.

Scalar Quantities Scalar quantities are measurements that have only magnitude (size) but no direction. Examples of scalar quantities are; Distance Speed.

10.2 Vectors in the Plane Warning: Only some of this is review.

10.2 day 1: Vectors in the Plane Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003 Mesa Verde National Park, Colorado.

8-6 Vectors Holt Geometry.

Honors Pre-Calculus 12.1 Vectors Page 419 Objective: Perform basic operations on vectors.

1. Math 160 Notes Packet #23 Vectors 2 Suppose a car is heading NE (northeast) at 60 mph. We can use a vector to help draw a picture (see right). 3.

Today, we will have a short review on vectors and projectiles and then have a quiz. You will need a calculator, a clicker and some scratch paper for the.

Vectors: Word Problems

8-5 Vectors Part 2: Adding and Applications. Resultants Vectors can also be named with a single lowercase letter, such as u. The map shows vectors representing.

Geometry 9.7 Vectors. Goals  I can name a vector using component notation.  I can add vectors.  I can determine the magnitude of a vector.  I can.

12.2 Vectors.  Quantities that have magnitude but not direction are called scalars. Ex: Area, volume, temperature, time, etc.  Quantities such as force,

A.) Scalar - A single number which is used to represent a quantity indicating magnitude or size. B.) Vector - A representation of certain quantities which.

Introduction to Vectors Section Vectors are an essential tool in physics and a very significant part of mathematics. Their primary application.

11. Section 12.1 Vectors Vectors What is a vector and how do you combine them?

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.

Holt Geometry 8-6 Vectors Warm Up Find AB. 1. A(0, 15), B(17, 0) 2. A(–4, 2), B(4, –2) Solve each equation. Round to the nearest tenth or nearest degree.

Section 6.3 Vectors 1. The student will represent vectors as directed line segments and write them in component form 2. The student will perform basic.

Vectors 3-1C What is a vector? What are the properties of vectors? How can a vector be a mathematical model for a trip?

Vectors Def. A vector is a quantity that has both magnitude and direction. v is displacement vector from A to B A is the initial point, B is the terminal.

Warm Up Find AB. 1. A(0, 15), B(17, 0) 2. A(–4, 2), B(4, –2)

Math 160 Notes Packet #23 Vectors. Math 160 Notes Packet #23 Vectors.

8-6 Vectors Holt McDougal Geometry Holt Geometry.

Intro to Vectors I. Vectors.

10.2 Vectors in a Plane Mesa Verde National Park, Colorado

10.2 day 1: Vectors in the Plane

Vectors Objective Students will be able to use basic vector operations to solve problems.

8-6 Vectors Warm Up Lesson Presentation Lesson Quiz Holt Geometry.

10.2 Vectors in a Plane Mesa Verde National Park, Colorado

Day 77 AGENDA: DG minutes.

Enduring Understanding: Modeling is widely used to represent physical and kinematic information. Essential Question: What are the practical applications.

Only some of this is review.

Vectors Accelerated Math 3.

Precalculus PreAP/Dual, Revised ©2017

Notes: 8-1 Geometric Vectors

Chapter 9.1 Notes: Translate Figures and Use Vectors

Lesson 63 Introduction to Vectors Lesson #1: Vectors are not rays.

8-6 Vectors Warm Up Lesson Presentation Lesson Quiz Holt Geometry.

Notes: 8-1 Geometric Vectors

Presentation transcript:

VECTORSVECTORS Describing paths

VECTOR: line segment with… i. Direction(an angle) ii. Magnitude||v|| = length of vector (distance)

EX: AB Point A is the origin or initial point Point B is the endpoint or terminal point A B

A B Basic terminology and notation: v Let v = A B ZERO VECTOR: ||v|| = 0

EQUAL VECTORS: Same magnitude & direction

Also Equal

NOT EQUAL

VECTOR SUM: XY + YZ = XZ X Y Z

Opposite vectors: v - w v w -w

Notationv = 3 right, 4 up from initial point

w = V =

EX 1: Graph 2v -3w

a b || V || = ? || v || = Magnitude or length

APPLICATION PROBLEMS Write a vectors representing the situation and draw the resulting trip. A small motorboat in still water maintains a speed of 10 mph. When the boat heads directly across a river it is perpendicular to the 4mph current. At what speed will the boat actually be travelling?

The Resultant Velocity is the sum of the two Velocities current boat

VECTOR ANGLE EXAMPLE: Sketch a vector 60 degrees North of East

THE DOT (scalar) PRODUCT v · w = a 1 a 2 + b 1 b 2 v = w =

EXAMPLES: FIND: v · w w · v v · v w · w v = w =