Vector Addition

Vector Addition Screenshot
  • Vectors
  • Vector Components
  • Vector Addition
Flash Logo Original Sim and Translations

Topics

  • Vectors
  • Vector Components
  • Vector Addition
  • Equations

Description

Explore vectors in 1D or 2D, and discover how vectors add together. Specify vectors in Cartesian or polar coordinates, and see the magnitude, angle, and components of each vector. Experiment with vector equations and compare vector sums and differences.

Sample Learning Goals

  • Describe a vector in your own words
  • Explain a method to add vectors
  • Compare and contrast the component styles
  • Decompose a vector into components
  • Describe what happens to a vector when it is multiplied by a scalar
  • Arrange vectors graphically to represent vector addition or subtraction

Standards Alignment

Common Core - Math

HSN-VM.A.1
(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
HSN-VM.A.2
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
HSN-VM.B.4
(+) Add and subtract vectors.
HSN-VM.B.4a
Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
HSN-VM.B.4b
Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
HSN-VM.B.4c
Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
HSN-VM.B.5
(+) Multiply a vector by a scalar.
HSN-VM.B.5a
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
HSN-VM.B.5b
Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
Version 1.0.0

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

Concept questions for Physics using PhET (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
MC Physics
Algebra-based Physics Semester one lessons, clicker questions, and schedule in pdf (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
Demo
HW
Lab
Physics
Vector Addition 1: Introduction to vector math (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
UG-Intro
Lab Mathematics
Physics
Vector Addition 2: Understanding Force equilibrium (Inquiry Based) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein UG-Intro
HS
Other Physics
Mathematics
equilibrium of forces tahani sarayreh UG-Intro
HS
Lab
Remote
Physics
Forces at equilibrium Nawal Nayfeh HS
UG-Intro
Lab
Remote
Physics
Find The components of a vector Dr Akhlaq Ahmad HS Lab
HW
Mathematics
Physics
Addition of Vectors by its Components Dr Akhlaq Ahmad UG-Intro
MS
HS
K-5
Lab
HW
Physics
Clases Demostrativas Interactivas (ILD) de Vectores A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Diana López UG-Intro
HS
Discuss
Demo
Physics
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López HS
MS
Other Chemistry
Physics
Biology
Mathematics
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. Diana López UG-Intro
HS
Other Physics
Mathematics
Chemistry
Soma de Vetores Juciane1 Matrtins HS Lab Physics
Figuras y cuerpos geométricos. Andrés Gualberto Palomo Cuevas HS Remote
HW
Mathematics
Guia de aprendizaje sobre vectores en simuladores jorge luis rodriguez acosta MS Guided Mathematics
Reforzamiento de vectores Andrés Gualberto Palomo Cuevas HS Lab Physics

Language Download or Run Tips
Albanian All shqip Run now Mbledhja e vektorëve
Azerbaijani All Azerbaijani Run now Vektorların toplanması
Basque All Euskara Run now Bektore-batuketa
Bosnian All Bosanski Run now Sabiranje vektora
Chinese (Simplified) All 中文 (中国) Run now 向量相加
Chinese (Traditional) All 中文 (台灣) Run now Vector Addition_向量的加法
Croatian All hrvatski Run now Zbrajanje vektora
Czech All čeština Run now Sčítání vektorů
Danish All Dansk Run now Vektor-addition
Dutch All Nederlands Run now Optellen van vectoren
French All français Run now Addition de vecteur 
German All Deutsch Run now Vektor Addition
Greek All Ελληνικά Run now Προσθήκη διανύσματος
Hebrew All עברית Run now חיבור וקטורים
Hindi All हिंदी Run now सदिशों का योग 
Hungarian All magyar Run now Vektorösszeadás
Italian All italiano Run now Somma vettoriale
Japanese All 日本語 Run now ベクトル加算
Kazakh All Kazakh Run now Векторларды қосу
Korean All 한국어 Run now 벡터 더하기
Mongolian All Монгол (Монгол) Run now Векторын Нийлбэр
Norwegian Bokmal All Norsk bokmål Run now Vektorsum
Persian All فارسی Run now جمع برداری
Polish All polski Run now Dodawanie wektorów
Portuguese (Brazil) All português (Brasil) Run now Adição de Vetores Download teacher tips PDF
Russian All русский Run now Сложение векторов
Serbian All Српски Run now Сабирање вектора
Slovak All Slovenčina Run now Skladanie vektorov
Spanish All español Run now Adición de Vectores Download teacher tips PDF
Spanish (Mexico) All español (México) Run now Adición de Vectores Download teacher tips PDF
Spanish (Peru) All español (Perú) Run now Adición de Vectores
Thai All ไทย Run now การรวมเวกเตอร์
Turkish All Türkçe Run now Vektör Ekleme
Ukrainian All українська Run now Додавання векторів Download teacher tips PDF
Vietnamese All Tiếng Việt Run now Cộng vector

HTML5 sims can run on iPads and Chromebooks, as well as PC, Mac, and Linux systems.

iPad:
iOS 12+ Safari
iPad compatible sims

Android:
Not officially supported. If you are using the HTML5 sims on Android, we recommend using the latest version of Google Chrome.

Chromebook:
Latest version of Google Chrome
The HTML5 and Flash PhET sims are supported on all Chromebooks.
Chromebook compatible sims

Windows Systems:
Microsoft Edge, latest version of Firefox, latest version of Google Chrome.

Macintosh Systems:
macOS 10.9.5+, Safari 9+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

Design Team Third-party Libraries Thanks To
  • Brandon Li (developer)
  • Chris Malley (developer)
  • Martin Veillette (developer)
  • Amy Rouinfar (lead designer)
  • Michael Dubson (original designer)
  • Diana López Tavares
  • Amanda McGarry
  • Ariel Paul
  • Kathy Perkins
  • almond-0.2.9.js
  • base64-js-1.2.0.js
  • FileSaver-b8054a2.js
  • font-awesome-4.5.0
  • game-up-camera-1.0.0.js
  • he-1.1.1.js
  • himalaya-0.2.7.js
  • jama-1.0.2
  • jquery-2.1.0.js
  • lodash-4.17.4.js
  • pegjs-0.7.0.js
  • seedrandom-2.4.2.js
  • text-2.0.12.js
  • TextEncoderLite-3c9f6f0.js