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

Slides:

Advertisements

Similar presentations

Introduction to Vectors

Advertisements

1/16/ : Coordinates in 3 Dimensions 6.4: Coordinates in Three Dimensions Expectations: G1.1.5: Given a segment in terms of its endpoints, determine.

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

constructions A Straight Line constructions Task: Task: Construct a line XY of length 5.9 cm. X  Construct a line more than 5.9 cm long (about 8 cm).

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

Points, Lines, and Planes

Introduction to Vectors. Overview Definition of a Vector Uses of Vectors Vector Notation Parts of Vectors.

The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane are.

Chapter 1.7 Midpoint and Distance in a Coordinate Plane

Tools of Geometry Chapter 1 Vocabulary Mrs. Robinson.

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

 Give an example of a point, line and plane that can be found in the classroom.

Basics. Undefined terms Point: a dot, no dimension Line: a line the an arrow on each end, one dimension Plane: two dimensions.

Section 1-3 Segments, Rays, and Distance. line; segment; ray;

9-2 Translations You found the magnitude and direction of vectors. Draw translations. Draw translations in the coordinate plane.

Vector Addition And Distance vs. Displacement. Distance and Displacement In Physics there is a difference between distance and displacement. Distance:

Bell Ringer on Lesson questions In your notes, then do p , 58, 61 and 63.

1.3 Segments and Their Measures Learning Targets: I can use segment postulates. I can use the Distance Formula to measure distances.

Bellwork Name all the angles that have the vertex B. 1) 2) 3) 4) a. Translate

Perform Congruence Transformations. A __________________ is an operation that moves or changes a geometric figure to produce a new figure called an __________.

1.2 Points, Lines, and Planes. What is a definition? Known words used to describe a new word Known words used to describe a new word Undefined terms –

8.1 and 8.2 answers. 8.3: Vectors February 9, 2009.

Two Dimensional Motion we will now analyze motion in the horizontal plane which (like all planes) is two dimensional we will first use vector diagrams.

Vectors have magnitude AND direction. – (14m/s west, 32° and falling [brrr!]) Scalars do not have direction, only magnitude. – ( 14m/s, 32° ) Vectors tip.

Geometry Lesson 1 – 2 Linear Measure Objective: Measure segments. Calculate with measures.

© 2013 Pearson Education, Inc. 12G Vectors in Space.

What is a locus? What is the relationship between a perpendicular bisector of a segment and the segment’s endpoints? What is the relationship between the.

LESSON FOUR: SEGMENTS AND SKEW LINES AND VECTORS…OH MY!!!

3/15/ : The Distance Formula 5.6: The Distance Formula and the Method of Quadrature Expectation: G1.1.5: Given a line segment in terms of its endpoints.

Starter Vocabulary Term What is distance? What is displacement? What is frame of reference? What is speed? What is velocity? What is acceleration? Definition.

1.1:Identify Points, Lines, & Planes 1.2:Use Segments & Congruence Objectives: 1.To learn the terminology and notation of the basic building blocks of.

1.1 Points, Lines, & Planes p. 6. What is a definition? Known words used to describe a new word Known words used to describe a new word Undefined terms.

1-3 Segments, Rays, and Distance

{ Constructions Duplicating and Line and an Angle.

Slide 1-1 Copyright © 2014 Pearson Education, Inc. 1.6 Constructions Involving Lines and Angles.

Section 1.1 Points, Lines, and Planes 11/22/2016.

 TEKS Focus:  (4)(A) Distinguish between undefined terms, definitions, postulates, conjectures, and theorems.  (1)(D) Communicate mathematical ideas,

Warm – up True / false : If false, explain why

Vectors, Operations, and the Dot Product

Foundations of Geometry

Warm – up True / false : If false, explain why

1.3 Segments and Their Measures

Distance vs. Displacement Speed vs. Velocity

Sect 7.4 Translations and Vectors

Segments, Rays, and Distance

COORDINATE PLANE.

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

9.1 Lines and Angles.

Warm – up True / false : If false, explain why

Let’s Get It Started Find the next two terms and describe the sequence in words: 5, 25, 125, 625, , 1, 4, 9, 16, 25, , 3,125 and 15,625.

Warm-Up: Common Words What are “common words” we use in everyday conversation? Do you have to think about their meaning? What if you didn’t know these.

4.2 Reflections Goals: Perform Reflections Perform Glide Reflections

Lines, Line Segments, Rays.

Teacher Note When talking about the midpoint, mention that it BISECTS the line segment.

Linear Measure Line Segment - A measurable part of a line that consists of two points, called the endpoints, and all the points between them. A segment.

Chapter 1 : Essentials of Geometry

Let’s Get It Started Find the next two terms and describe the sequence in words: 5, 25, 125, 625, , 1, 4, 9, 16, 25, , 3,125 and 15,625.

1.2 Informal Geometry and Measurement

Chapter 9.1 Notes: Translate Figures and Use Vectors

Point Line Ray Line Segment Plane

January 20 and January 21 Perimeters and Areas

Section 1.4 Measuring Segments and Angles

The most basic figures in geometry are undefined terms, which cannot be defined by using other figures. The undefined terms point, line, and plane.

Unit 4 Reflect, Translate & Rotate

Bell work What is the least number of line segments you can draw end to end to connect the nine dots on the grid?

Geometry (Lines) SOL 4.14, 4.15, 4.16 lines, segments, rays, points, angles, intersecting, parallel, & perpendicular 4.14 The student will investigate.

Geometry Unit 1: Foundations

Lines, Line Segments, Rays and Angles

1.3 Early Definitions & Postulates

Presentation transcript:

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

Definition The vector AB is a model of the straight line path from point A to point B. A B Origin Endpoint A vector is a “directed” line segment, useful in describing paths. A vector looks like a ray, but it is NOT!! A vector has both direction and length.

Direction and Length From the school entrance, I went three blocks north. The distance is: Three blocks The direction is: North

Direction and Length The length of AB is the distance between A and B. The direction of a vector is measured counterclockwise from the horizonal (positive x-axis).

Drawing Vectors Draw vector YZ with direction of 45° and length of 10 cm. 1.Draw a horizontal dotted line 2.Use a protractor to draw 45° 3.Use a ruler to draw 10 cm 4.Label the points 45° Y Z 10 cm

Try It Turn to page 166 in your book. You will need a protractor and ruler. Direction 138° Length 2.7 cm

Vector Sum A path or trip that consists of several segments can be modeled by a sequence of vectors. The endpoint of one vector is the origin of the next vector in the chain. The figure shows a ship’s path from point M to point N that consists of five vectors. M S T U V N

Vector Sum What is the shortest path from M to N? Write the vector sum for the boat’s trip starting with MS M S T U V N

For vector sums, the following is true: XY + YZ = XZ X Y Z

Vector vs Ray How is a vector similar to a ray? Both have starting point and a direction. How is a vector different from a ray? A vector has a length: a ray goes on forever. vs Vector Ray

What is a vector? A vector is a directed line segment with a direction and length. What are the properties of vectors? Vectors have direction and length. How can a vector be a mathematical model for a trip? When you go on a trip, you go in a direction for a certain number of miles.

Assignment Page 168, 1-9, 17-21