Difference between revisions of "PhET-Simulations-for-Mathematics/C2/Vector-Addition/English"

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(Created page with " '''Title of the script''': '''Vector Addition''' '''Author''': Shraddha Kodavade '''Keywords''': Phet simulation, vector, number line, Cartesian plane, vector addition, sca...")
 
 
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'''Keywords''': Phet simulation, vector, number line, Cartesian plane, vector addition, scalar multiplication, angle, solve equations, video tutorial.
 
'''Keywords''': Phet simulation, vector, number line, Cartesian plane, vector addition, scalar multiplication, angle, solve equations, video tutorial.
−
 
  
 
{|border=1
 
{|border=1
−
 
 
||'''Visual Cue'''
 
||'''Visual Cue'''
 
||'''Narration'''
 
||'''Narration'''
−
 
 
|-
 
|-
 
|| '''Slide Number 1'''
 
|| '''Slide Number 1'''
  
 
'''Title Slide'''
 
'''Title Slide'''
−
|| Welcome to this spoken tutorial on '''Vector Addition'''.
+
|| Welcome to this spoken tutorial on '''Vector Addition.'''
−
 
+
 
|-  
 
|-  
 
|| '''Slide Number 2'''
 
|| '''Slide Number 2'''
Line 28: Line 24:
 
§ Vector Addition and Scalar multiplication
 
§ Vector Addition and Scalar multiplication
  
−
§ How to arrange vectors graphically to represent vector addition or subtraction.
+
§ How to arrange vectors graphically to represent vector addition or subtraction
 
|-  
 
|-  
 
|| '''Slide Number 3'''
 
|| '''Slide Number 3'''
Line 46: Line 42:
 
|| To follow this tutorial,
 
|| To follow this tutorial,
  
−
Learners should be familiar with topics in basic mathematics.
+
Learner should be familiar with topics in basic mathematics.
  
−
Please use the link below to access the tutorials on '''PhET Simulations'''.
+
Please use the link below to access the tutorials on PhET Simulations.
 
|-  
 
|-  
 
|| '''Slide Number 5'''
 
|| '''Slide Number 5'''
  
−
'''Link for Phet Simulations'''
+
Link for Phet Simulations
  
 
'''[https://phet.colorado.edu/en/ https://phet.colorado.edu/en/simulations/vector-addition]'''
 
'''[https://phet.colorado.edu/en/ https://phet.colorado.edu/en/simulations/vector-addition]'''
 +
|| Please use the given link to download the '''PhET simulation'''.
  
−
|| Please use the given link to download the '''PhET simulations'''.
 
  
 
|-  
 
|-  
Line 68: Line 64:
  
 
'''PhET Simulations '''
 
'''PhET Simulations '''
−
 
 
|| In this tutorial, we will use,
 
|| In this tutorial, we will use,
  
 
'''Vector Addition PhET Simulation'''.
 
'''Vector Addition PhET Simulation'''.
 
|-  
 
|-  
−
|| Point to the file in the '''Downloads''' folder.
+
|| Point to the file in the Downloads folder.
  
−
'''Vector Addition PhET simulation'''
+
'''Vector Addition PhETSimulations'''
 
|| I have already downloaded the '''Vector Addition simulation''' to my '''Downloads''' folder.
 
|| I have already downloaded the '''Vector Addition simulation''' to my '''Downloads''' folder.
 
|-  
 
|-  
−
|| Only Narration.
+
||  
−
|| Let us begin with '''Vector Addition ''' to understand the vectors. better.
+
|| Let us begin with '''Vector Addition ''' to understand the vectors better.
 
|-  
 
|-  
 
|| Right-click on the simulation.
 
|| Right-click on the simulation.
  
−
Select the '''Open With Firefox Web Browser ''' option.
+
Select the '''Open With Chrome Browser ''' option.
  
 
Point to the browser address.
 
Point to the browser address.
Line 95: Line 90:
 
|| This is the interface of '''Vector Addition simulation'''.
 
|| This is the interface of '''Vector Addition simulation'''.
 
|-  
 
|-  
−
|| Point to each option on the screen.
+
|| Point to each option on the screen
 
|| The interface has four screens,
 
|| The interface has four screens,
  
Line 107: Line 102:
 
|-  
 
|-  
 
|| Click on the''' 1D '''screen.
 
|| Click on the''' 1D '''screen.
−
|| First, let us explore the '''1D ''' simulation.
+
|| First, let us explore '''1D ''' simulation.
 
|-  
 
|-  
 
|| The point on the black number line.
 
|| The point on the black number line.
Line 123: Line 118:
 
|-  
 
|-  
 
|| Drag the vectors on the '''Cartesian plane'''.
 
|| Drag the vectors on the '''Cartesian plane'''.
−
|| Let us drag and place the vector '''a''', '''b''' and '''c''' on the '''Cartesian plane'''.
+
|| Let us drag and place the vector a, b and c on the '''Cartesian plane'''.
 
|-  
 
|-  
 
|| Click on the '''Values''' check box.
 
|| Click on the '''Values''' check box.
Line 158: Line 153:
 
A new vector ‘'''s'''’ appears on the number line.  
 
A new vector ‘'''s'''’ appears on the number line.  
 
|-  
 
|-  
−
|| Drag and arrange vectors '''a''', '''b''' and '''c'''.
+
|| Drag and arrange vectors a,b and c
−
|| Arrange vectors '''a''', '''b''' and '''c''', a unit distance above vector ''' s'''.
+
|| The initial point of vector '''a''' coincides with that of vector '''s'''.  
−
 
+
−
The initial point of vector '''a''' coincides with that of vector '''s'''.  
+
  
 
The tail of '''a''' meets the starting point of vector '''b'''.  
 
The tail of '''a''' meets the starting point of vector '''b'''.  
Line 171: Line 164:
 
|-  
 
|-  
 
|| Drag vector a
 
|| Drag vector a
−
|| Reverse the direction of vector '''a''' by dragging the arrow tip of vector '''a''' to the negative direction of the axis.
+
|| Reverse the direction of vector '''a''' by dragging the arrow tip of '''a''' to the negative direction of the axis.
  
 
The '''x''' value becomes -10.
 
The '''x''' value becomes -10.
Line 185: Line 178:
 
|-  
 
|-  
 
|| Drag vector a
 
|| Drag vector a
−
|| Change vector ''' a''' to 5 units in opposite direction.  
+
|| Change the vector ''' a''' 5 units in opposite direction.  
  
 
The '''s''' value also changes and takes up 5 units.
 
The '''s''' value also changes and takes up 5 units.
 
|-  
 
|-  
 
|| Click on the 2D screen.
 
|| Click on the 2D screen.
−
|| Next let us click on the '''Explore 2D ''' screen.
+
|| Let us click on the '''Explore 2D ''' screen.
  
−
On this screen, we see a '''Cartesian''' system of axes.
+
On this screen, we can see a '''Cartesian''' system of axes.
 
|-  
 
|-  
 
|| Point to the bottom right side.
 
|| Point to the bottom right side.
Line 224: Line 217:
 
|-  
 
|-  
 
|| Point to the Components section.
 
|| Point to the Components section.
−
|| On the right side of the screen we can see 4 options under '''Components'''.
+
|| On the right side of the screen we can see 4 options under the '''Components'''.
  
 
|-  
 
|-  
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We can see that base and height get annotated for each vector.  
 
We can see that base and height get annotated for each vector.  
  
−
The coordinate values of the vectors are shown on the axes.  
+
The coordinate values of vector are shown on the axes.  
  
 
|-  
 
|-  
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Point to vector e.
 
Point to vector e.
−
|| For vector '''d''', let us take magnitude as 6 and angle as 50 degrees.
+
|| For vector '''d''', let us take the magnitude as 6 and angle as 50 degrees.
  
−
For vector '''e''', let it be 7 and -30 degrees.
+
For vector '''e''', let it be 7 and -30.
 
|-  
 
|-  
−
|| Move vector’s tail to the tip of vector '''d'''.
+
|| Move vector’s tail to the tip of vector d
 
|| Drag and place the vector’s tail to touch the tip of vector '''d'''.
 
|| Drag and place the vector’s tail to touch the tip of vector '''d'''.
 
|-  
 
|-  
Line 275: Line 268:
  
 
Point to vector '''s'''.
 
Point to vector '''s'''.
−
|| Drag the tip of vector ''' s''' to the tip of '''d'''.  
+
|| Drag the tip of vector ''' s''' to tip of '''d'''.  
  
−
A triangle is formed. The vector '''s ''' represents the net displacement between the vectors '''d '''and '''e'''.
+
A triangle is formed.
 +
 
 +
The vector '''s ''' represents the net displacement between vectors '''d ''' and '''e'''.
 
|-  
 
|-  
−
|| Drag vector '''f'''.
+
|| Drag vector f
  
  
 
Point to the triangle formed.
 
Point to the triangle formed.
−
|| Replace vector ''' s''' with '''f''' that is still to be used from the vectors list.  
+
|| Replace vector''' s''' with vector '''f''' that is still to be used from the vectors list.  
  
−
Change the direction of '''f'''.
+
Change the direction of vector '''f'''.
  
−
A closed path of direction is formed, where all vectors travel in the same direction.
+
A closed path is formed, where all the vectors travel in the same direction.
 
|-  
 
|-  
 
|| Point to vector '''s'''.
 
|| Point to vector '''s'''.
−
|| We notice that the vector '''s''' disappears.
+
|| We notice that vector '''s''' disappears.
  
 
This is because the initial and terminal points of this triangle coincide.  
 
This is because the initial and terminal points of this triangle coincide.  
Line 298: Line 293:
 
|| Click on the '''Equations''' screen.
 
|| Click on the '''Equations''' screen.
 
Point to vector equations  
 
Point to vector equations  
−
|| Now let’s click on the '''Equations''' screen.
+
|| Now let us click on the '''Equations''' screen.
  
 
In this screen vector addition and scalar multiplication are used to form equations.
 
In this screen vector addition and scalar multiplication are used to form equations.
Line 312: Line 307:
 
|| The first option takes coordinate values with respective to '''x''' and '''y''' axis for each vector.  
 
|| The first option takes coordinate values with respective to '''x''' and '''y''' axis for each vector.  
  
−
The second system takes the angle with respect to the '''x''' axis and unit magnitude.
+
The second system takes the angle with respect to '''x''' axis and unit magnitude.
 
|-  
 
|-  
 
|| Point to the second option.
 
|| Point to the second option.
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|| This simulation can solve three different vector addition equations for us.
 
|| This simulation can solve three different vector addition equations for us.
  
−
Here we have three vectors '''d''',''' e''' and '''f'''.
+
Here we have vectors '''d''',''' e''' and '''f'''.
  
 
It can solve for us '''d + e = f'''
 
It can solve for us '''d + e = f'''
Line 343: Line 338:
 
|| Select '''d-e=f '''.
 
|| Select '''d-e=f '''.
  
−
Click on base vectors option.
+
Click on '''Base Vectors''' option.
−
 
+
−
Click on the '''Values''' check box.
+
  
 +
Click on the Values check box.
 
|| Select '''d-e=f'''.
 
|| Select '''d-e=f'''.
  
−
Choose base vectors options.
+
Choose '''Base Vectors''' option.  
−
 
+
−
Choose '''d ''' magnitude as 10 and angle 0.  
+
  
 +
Choose '''d '''magnitude as 10 and angle 0.
 +
 
Choose '''e''' magnitude as 4 and angle 0.  
 
Choose '''e''' magnitude as 4 and angle 0.  
  
Line 359: Line 353:
 
Click on the '''Values''' check box.
 
Click on the '''Values''' check box.
 
|-  
 
|-  
−
|| Move vector '''d''' to y axis = 10
+
|| Move vector d to y axis=10
  
−
Move vector '''e''' at y axis = 5
+
Move vector e at y axis=5
  
−
Move vector f at the tail of vector '''e'''.
+
Move vector f at the tail of vector e.
−
|| Place vector ''' d ''' on line with y axis =10.  
+
|| Place vector ''' d '''on line with y axis =10.  
  
−
Place vector '''e''' with its initial point same as''' d''' at '''y ''' axis = 5.  
+
Place vector '''e''' with its initial point as''' d''' at '''y ''' axis=5.  
  
 
Place vector '''f'''’s initial point at the tail of vector '''e'''.
 
Place vector '''f'''’s initial point at the tail of vector '''e'''.
 
|-  
 
|-  
 
|| Point to the resultant vector.
 
|| Point to the resultant vector.
−
|| The resultant output represents the difference between vectors '''d''' and '''e'''.
+
|| The resultant output represents the difference between vector d and e.
 
|-  
 
|-  
−
|| Click on '''d+e+f=0'''.
+
|| Click on d+e+f=0.
−
|| Click on''' d+e+f=0'''.  
+
|| Click on ''' d+e+f=0'''.  
  
 
Here, the vector addition has sum 0.
 
Here, the vector addition has sum 0.
−
 
+
−
This implies that each vector is the negative sum of the other two.
+
This implies that each vector is negative sum of the other two.
 
|-  
 
|-  
−
|| Move vector '''f''' to '''y''' axis=10
+
|| Move vector f to y axis=10
  
−
Move vector '''d''' and '''e''' to '''y''' axis=5
+
Move vector d and e to y axis=5
−
|| Place the vector ''' f '''on the '''y ''' = 10 axis line.  
+
|| Place the vector ''' f ''' on y=10 axis line.  
  
−
Place vector ''' d''' and vector '''e''' next to each other at y=5 axis line with the initial point of '''d''' being at terminal point of ''' f'''.
+
Place vector ''' d''' and vector '''e''' next to each other at y=5 axis line with the initial point of '''d''' being at the terminal point of ''' f'''.
  
 
We can see that '''d+e=-f''', since '''f''' is in the opposite direction.  
 
We can see that '''d+e=-f''', since '''f''' is in the opposite direction.  
Line 393: Line 387:
 
|| Click on d-e=f.
 
|| Click on d-e=f.
  
−
Click on the arrows beside '''d''' and '''e'''.
+
Click on the arrows beside d and e
 
|| To perform scalar multiplication, click on the arrows beside vectors '''d '''and '''e'''.  
 
|| To perform scalar multiplication, click on the arrows beside vectors '''d '''and '''e'''.  
  
Line 425: Line 419:
 
|| As an assignment,
 
|| As an assignment,
  
−
Explore the Lab screen available at the bottom of the simulation.
+
Explore the '''Lab''' screen available at the bottom of the simulation.
 
|-  
 
|-  
 
|| '''Slide Number 10'''
 
|| '''Slide Number 10'''
Line 463: Line 457:
 
Point to the link
 
Point to the link
 
|| Please post your timed queries in this forum.
 
|| Please post your timed queries in this forum.
 +
 +
  
 
|-  
 
|-  
Line 469: Line 465:
 
'''Acknowledgement'''
 
'''Acknowledgement'''
 
|| The Spoken Tutorial project is funded by the Ministry of Education, Govt. of India
 
|| The Spoken Tutorial project is funded by the Ministry of Education, Govt. of India
−
|-  
+
|-   
−
|| '''Slide Number 14'''
+
−
 
+
−
'''Thank you'''
+
−
 
+
 
|| This is Shraddha Kodavade, a '''FOSSEE''' summer fellow 2022, IIT Bombay signing off.  
 
|| This is Shraddha Kodavade, a '''FOSSEE''' summer fellow 2022, IIT Bombay signing off.  
  

Latest revision as of 18:05, 2 November 2023

Title of the script: Vector Addition

Author: Shraddha Kodavade

Keywords: Phet simulation, vector, number line, Cartesian plane, vector addition, scalar multiplication, angle, solve equations, video tutorial.

Visual Cue Narration
Slide Number 1

Title Slide

Welcome to this spoken tutorial on Vector Addition.
Slide Number 2

Learning Objectives

In this tutorial, we will learn about:

§ 1D and 2D dimensions of a vector

§ Vector Addition and Scalar multiplication

§ How to arrange vectors graphically to represent vector addition or subtraction

Slide Number 3

System Requirements

This tutorial is recorded using,

Windows 10-64-bit operating system

Chrome version 101.0.49

Slide Number 4

Pre-requisites

https://spoken-tutorial.org

To follow this tutorial,

Learner should be familiar with topics in basic mathematics.

Please use the link below to access the tutorials on PhET Simulations.

Slide Number 5

Link for Phet Simulations

https://phet.colorado.edu/en/simulations/vector-addition

Please use the given link to download the PhET simulation.


Slide Number 6

Vector

A vector is a quantity that has both magnitude and direction.
Slide Number 7

PhET Simulations

In this tutorial, we will use,

Vector Addition PhET Simulation.

Point to the file in the Downloads folder.

Vector Addition PhETSimulations

I have already downloaded the Vector Addition simulation to my Downloads folder.
Let us begin with Vector Addition to understand the vectors better.
Right-click on the simulation.

Select the Open With Chrome Browser option.

Point to the browser address.

To open the simulation, right-click on the downloaded simulation.

Select the option, Open With Chrome Browser.

The file opens in browser.

Cursor on the interface. This is the interface of Vector Addition simulation.
Point to each option on the screen The interface has four screens,

Explore 1D

Explore 2D

Lab and

Equations.

Click on the 1D screen. First, let us explore 1D simulation.
The point on the black number line.

Click on the horizontal and vertical axis buttons.

A black-colored number line is visible on the screen.

We can switch between the horizontal and the vertical number lines.

Click on the horizontal axis. Let us choose the horizontal axis.
Point to the vectors image We can see three vectors available for our use on the interface.
Drag the vectors on the Cartesian plane. Let us drag and place the vector a, b and c on the Cartesian plane.
Click on the Values check box. Click on the Values check box.

The magnitude of each vector appears on the vector.

Select vector a.

Its specifications are listed in the top box.

Point to the magnitude.

Point to the angle.

Drag the arrow head to increase the size of the vector.

Point to the x value

Point to the y value.

By default, the magnitude is 5 units.

The angle is 0 with respect to x axis.

Let us change the magnitude to 10 units, the value of x changes as well.

y value remains 0 due to the absence of the vertical axis.

Click on the Sum check box.

Point to vector s.

Click on the Sum check box.

A new vector ‘s’ appears on the number line.

Drag and arrange vectors a,b and c The initial point of vector a coincides with that of vector s.

The tail of a meets the starting point of vector b.

Similarly the tail of vector b meets the starting point of vector c.

Point to vector s This vector represents the vector addition, that is a+b+c is equal to vector s.
Drag vector a Reverse the direction of vector a by dragging the arrow tip of a to the negative direction of the axis.

The x value becomes -10.

Point to vector s.

a=-b-c.

We can see that the vector s vanishes.

This happens because a is equal to minus b, minus c.

Drag vector a Change the vector a 5 units in opposite direction.

The s value also changes and takes up 5 units.

Click on the 2D screen. Let us click on the Explore 2D screen.

On this screen, we can see a Cartesian system of axes.

Point to the bottom right side.

Click on the blue option.

Drag and place the vectors in the plane.

Click on the pink option.

Drag and place the vectors in the plane.

Point to vector d, e and f

There are two options visible at the bottom right corner.

Click on the blue option.

Drag and place the vectors in the plane.

The vectors get labeled as a, b and c.

The top box shows the various parameter values for the selected vector.

Click on the pink button.

Drag and place the vectors in the plane.

They get labeled as d, e, and f.

On this screen, there is no difference between the two options.

Point to the Components section. On the right side of the screen we can see 4 options under the Components.
Show the annotation by clicking the second option. Let us choose the second option.

Here for each vector, perpendiculars are drawn from the base to its tip.

Show the annotation by clicking the third option. Let us choose the third option.

We can see that base and height get annotated for each vector.

The coordinate values of vector are shown on the axes.

Click on the hidden eye option. Select the hidden eye option and remove vector f from the screen.
Point to vector d.

Point to vector e.

For vector d, let us take the magnitude as 6 and angle as 50 degrees.

For vector e, let it be 7 and -30.

Move vector’s tail to the tip of vector d Drag and place the vector’s tail to touch the tip of vector d.
Click on sum

Point to vector s

Click on the Sum check box.

A new vector s appears.

Point to the displacement vector This addition is different from the previous one.

Earlier, a linear addition took place where the angle for all vectors was 0.

The addition taking place on the screen is an example of displacement vector.

A displacement vector gives the change in position.

Drag the tip of vector s to the tip of d.

Point to the triangle formed.

Point to vector s.

Drag the tip of vector s to tip of d.

A triangle is formed.

The vector s represents the net displacement between vectors d and e.

Drag vector f


Point to the triangle formed.

Replace vector s with vector f that is still to be used from the vectors list.

Change the direction of vector f.

A closed path is formed, where all the vectors travel in the same direction.

Point to vector s. We notice that vector s disappears.

This is because the initial and terminal points of this triangle coincide.

This leads to zero resultant.

Click on the Equations screen.

Point to vector equations

Now let us click on the Equations screen.

In this screen vector addition and scalar multiplication are used to form equations.

Point to the bottom right options. There are two options to specify the base vector's parameter values.

The difference between the two lies in the input it takes from the user.

Point to the blue option in the bottom right.

Point to the pink option in the bottom right.

The first option takes coordinate values with respective to x and y axis for each vector.

The second system takes the angle with respect to x axis and unit magnitude.

Point to the second option.

Click on the pink box at bottom right.

Let us choose the second option.

Click on the pink box at the bottom right.

Point to the selected vector box

Point to the formula box on the top most part.

Drag and place the vectors in the plane.

This simulation can solve three different vector addition equations for us.

Here we have vectors d, e and f.

It can solve for us d + e = f

It can solve for us d - e = f and

d + e +f =0.

Select d+e=f . Let us understand each equation type.

d+e=f is the vector addition that we explored in 2D screen.

Select d-e=f .

Click on Base Vectors option.

Click on the Values check box.

Select d-e=f.

Choose Base Vectors option.

Choose d magnitude as 10 and angle 0.

Choose e magnitude as 4 and angle 0.

The vector f appears.

Click on the Values check box.

Move vector d to y axis=10

Move vector e at y axis=5

Move vector f at the tail of vector e.

Place vector d on line with y axis =10.

Place vector e with its initial point as d at y axis=5.

Place vector f’s initial point at the tail of vector e.

Point to the resultant vector. The resultant output represents the difference between vector d and e.
Click on d+e+f=0. Click on d+e+f=0.

Here, the vector addition has sum 0.

This implies that each vector is negative sum of the other two.

Move vector f to y axis=10

Move vector d and e to y axis=5

Place the vector f on y=10 axis line.

Place vector d and vector e next to each other at y=5 axis line with the initial point of d being at the terminal point of f.

We can see that d+e=-f, since f is in the opposite direction.

Therefore d+e+f=0.

Click on d-e=f.

Click on the arrows beside d and e

To perform scalar multiplication, click on the arrows beside vectors d and e.

This will stretch or shrink the vectors.

Let us try 2d-e=f.

Point to resultant vectors. The resultant shape of each vector is formed.
Narration With this, we have come to the end of this tutorial.

Let us summarise.

Slide Number 8

Summary

In this tutorial, we have learnt about,

§ 1D and 2D dimensions of a vector

§ How to perform Vector Addition and Scalar multiplication

§ How to arrange vectors graphically to represent vector addition or subtraction

Slide Number 9

Assignment

As an assignment,

Explore the Lab screen available at the bottom of the simulation.

Slide Number 10

About the Spoken Tutorial Project

The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.

Slide Number 11

Spoken Tutorial workshops

The Spoken Tutorial Project team:

conducts workshops using spoken tutorials and

gives certificates on passing online tests.

For more details, please write to us.

Slide Number 12

Forum for specific questions:

Questions in THIS Spoken Tutorial?

Visit https://forums.spoken-tutorial.org}

Choose the minute and second where you have the question

Explain your question briefly

The Spoken Tutorial project will ensure an answer

You will have to register to ask questions

Point to the link

Please post your timed queries in this forum.


Slide Number 13

Acknowledgement

The Spoken Tutorial project is funded by the Ministry of Education, Govt. of India
This is Shraddha Kodavade, a FOSSEE summer fellow 2022, IIT Bombay signing off.

Thanks for joining.

Contributors and Content Editors

Madhurig

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