Section 4.1 – Vectors (in component form)

Slides:

Advertisements

Similar presentations

Vectors Maggie Ambrose Maddy Farber. Hook… Component Form of a Vector  If v is a vector in a plane whose initial point is the origin and whose terminal.

Advertisements

Chapter 10 Vocabulary.

Introduction to Vectors March 2, What are Vectors? Vectors are pairs of a direction and a magnitude. We usually represent a vector with an arrow:

10.6 Vectors in Space.

Digital Lesson Vectors.

Vectors Sections 6.6. Objectives Rewrite a vector in rectangular coordinates (in terms of i and j) given the initial and terminal points of the vector.

Geometry of R 2 and R 3 Vectors in R 2 and R 3. NOTATION RThe set of real numbers R 2 The set of ordered pairs of real numbers R 3 The set of ordered.

Copyright © Cengage Learning. All rights reserved.

APPLICATIONS OF TRIGONOMETRY

VECTORS. A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude.

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,

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.

Vectors. A line segment to which a direction has been assigned is called a directed line segment. The figure below shows a directed line segment form.

6.1 – Vectors in the Plane. What are Vectors? Vectors are a quantity that have both magnitude (length) and direction, usually represented with an arrow:

Problem of The Day A vector v of length 6 makes a 150 degree angle with the vector [1,0], when they are placed tail-to-tail. Find the components of v.

VECTORS. A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude.

Vectors in Plane Objectives of this Section Graph Vectors Find a Position Vector Add and Subtract Vectors Find a Scalar Product and Magnitude of a Vector.

Section 9.1 Polar Coordinates. x OriginPole Polar axis.

Vectors in Space. 1. Describe the set of points (x, y, z) defined by the equation (Similar to p.364 #7-14)

Chapter 8 VECTORS Review 1. The length of the line represents the magnitude and the arrow indicates the direction. 2. The magnitude and direction of.

Warm up 1. Find the magnitude of this vector 2. A vector has Initial point (0,2) and terminal point (9,15). Write this vector in component form. 3. Find.

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

Meeting 23 Vectors. Vectors in 2-Space, 3-Space, and n- Space We will denote vectors in boldface type such as a, b, v, w, and x, and we will denote scalars.

8.4 Vectors. A vector is a quantity that has both magnitude and direction. Vectors in the plane can be represented by arrows. The length of the arrow.

8.5.3 – Unit Vectors, Linear Combinations. In the case of vectors, we have a special vector known as the unit vector – Unit Vector = any vector with a.

Geometry Lesson 8 – 7 Vectors Objective: Find magnitudes and directions of vectors. Add and subtract vectors.

It’s time for Chapter 6… Section 6.1a Vectors in the Plane.

Section 6.6 Vectors. Overview A vector is a quantity that has both magnitude and direction. In contrast, a scalar is a quantity that has magnitude but.

11.1 Vectors in the Plane.  Quantities that have magnitude but not direction are called scalars. Ex: Area, volume, temperature, time, etc.  Quantities.

OBJECTIVES: Represent vectors as directed line segments Write the component forms of vectors Perform basic vector operations and represent them graphically.

Chapter – 6.5 Vectors.

Warm-Up 12/04 1. A. Rigor: You will learn how to represent and operate with vectors in the coordinate plane and to write a vector as a linear combination.

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

3.3 Vectors in the Plane. Numbers that need both magnitude and direction to be described are called vectors. To represent such a quantity we use a directed.

 A vector is a mathematical object that has both magnitude (size) and direction  Students will be able to use basic vector operations and the dot product.

Vectors 1] Vector A is 3.00 units in length and points along the positive x axis. Vector B is 4.00 units in length and points along the negative y axis.

We will use the distance formula and the law of cosines to develop a formula to find the angle between two vectors.

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

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.

11.5 Vectors in the Plane Do Now A man is at the top of a lighthouse 100 ft high and spots a ship in the ocean. His angle of depression to the ship is.

VECTORS. A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude.

Homework Questions. Chapter 6 Section 6.1 Vectors.

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.

CHAPTER 3 VECTORS NHAA/IMK/UNIMAP.

5.4 Vectors terminal point initial point Q v S w P R

11.1 Polar Coordinates.

Objective: Computing work.

Make sure your worksheet from Friday is complete and turn it in

Q Terminal Point Initial Point P Directed line segment.

VECTORS 6.6 “It’s a mathematical term, represented by

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

Scalars Some quantities, like temperature, distance, height, area, and volume, can be represented by a ________________ that indicates __________________,

8.6 Vectors in Space.

Notes: 8-1 Geometric Vectors

Section 3.1 – Vectors in Component Form

Day 79 AGENDA: DG minutes.

/s Fig. P3.18, p.72.

Copyright © Cengage Learning. All rights reserved.

8 Applications of Trigonometry Copyright © 2009 Pearson Addison-Wesley.

Section 6.1: Vectors in a Plane

Three Dimensional Geometry and Vectors

Honors Precalculus 4/19/18 IDs on and showing

Section 9.4 Vectors.

Notes: 8-1 Geometric Vectors

Lesson 83 – Algebraic Vectors

Presentation transcript:

Section 4.1 – Vectors (in component form) Vector – directed distance

Move vectors to the origin so that computations can be done. initial point terminalpoint

Magnitude of a vector – the length of the vector Find the magnitude of Find the magnitude of

Given , find:

Unit Vector – Vector whose magnitude is 1. Find the unit vector having the same direction as v. Find the unit vector having the same direction as v.

Write the vector v in the form ai + bj given its magnitude and the angle it makes with the positive x-axis. 8

Write the vector v in the form ai + bj given its magnitude and the angle it makes with the positive x-axis. 3