Vector addition by summing scalar components - easy

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William Haynes

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William Haynes

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Jay McCormack

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William Haynes 2 weeks, 6 days ago

Saved a checkpoint:

Replaced geogebra_file() with geogebra_applet() to work around bug

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William Haynes 1 month ago

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Bug Reported, applet not loading

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William Haynes 1 year, 2 months ago

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Revised diagram to allow dragging of the components. Revised logic to ensure that the vectors don't intersect.

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William Haynes 1 year, 2 months ago

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prior to change

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William Haynes commented 1 year, 2 months ago

Fixed typography for vectors.

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Jay McCormack 1 year, 7 months ago

Gave some feedback: Ready to use

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William Haynes 2 years, 6 months ago

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Bug report from Jay McCormack

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Jay McCormack 2 years, 6 months ago

Gave some feedback: Needs to be tested

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Jay McCormack 2 years, 6 months ago

Gave some feedback: Has some problems

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William Haynes 4 years, 2 months ago

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William Haynes 4 years, 7 months ago

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William Haynes 4 years, 7 months ago

Gave some feedback: Doesn't work

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William Haynes 4 years, 7 months ago

Gave some feedback: Needs to be tested

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William Haynes 4 years, 7 months ago

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William Haynes 6 years, 6 months ago

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William Haynes 6 years, 6 months ago

Created this.

Name	Status	Author	Last Modified
Vector addition by summing scalar components - easy	Ready to use	William Haynes	08/03/2025 17:27
Find magnitude and direction of three vectors	Ready to use	William Haynes	01/01/2021 00:53
Vector addition by summing scalar components	draft	Marie Nicholson	04/02/2021 15:37
Timur's copy of Vector addition by summing scalar components	draft	Timur Zaripov	03/04/2019 11:16
Timur's copy of Find magnitude and direction of three vectors	draft	Timur Zaripov	03/04/2019 11:24
Timur's copy of Vector addition by summing scalar components - easy	draft	Timur Zaripov	03/04/2019 11:27
Magnitude and direction of three vectors	draft	Maria Aneiros	25/05/2019 02:07
Maria's copy of Find magnitude and direction of three vectors	Ready to use	Maria Aneiros	25/05/2019 02:19
Vector addition by summing scalar components - easy	draft	Xiaodan Leng	10/07/2019 22:01
Find magnitude and direction of three vectors	draft	Xiaodan Leng	10/07/2019 22:02
Vector addition by summing scalar components	draft	Chris King	12/07/2019 05:09

There are 21 other versions that do you not have access to.

Question statement

Three forces, $\color{red}{\mathbf{A}}, \color{blue}{\mathbf{B}}\ \text{and } \color{forestgreen}{\mathbf{C}}$ are drawn to scale of 1 square = {scale} {units[1]}. Find the resultant by summing scalar components.

{applet}

Give any introductory information the student needs.

			Name	Type	Generated Value

FA	vector	vector(10,-9)
FB	vector	vector(-3,10)
FC	vector	vector(-1,2)
units	list	[ "ft", "lb" ]
scale	integer	4
B1	vector	vector(3,-4)
A1	vector	vector(-7,2)
C1	vector	vector(1,-7)
B2	vector	vector(0,6)
A2	vector	vector(3,-7)
C2	vector	vector(0,-5)

			Name	Type	Generated Value

FR	vector	vector(6,3)
theta	number	26.5650511771
resultant	quantity	quantity(26.832815729997476, "lbs")

			Name	Type	Generated Value

applet	ggbapplet	HTML node
params	dict	Dictionary with 7 entries
Z	integer	8
BC	boolean	false
AB	boolean	false
CA	boolean	false

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
A2-A1

JME function reference

Description

FA in first or fourth quadrant

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `vector`

vector(10,-9)

← Depends on:

→ Used by:

Advice
Variable testing condition
"Components of components" → "Ax" - Correct Quantity.
"Components of components" → "Ay" - Correct Quantity.

Parts

Components of components Gap-fill
Components of resultant Gap-fill
1. Gap Rx Engineering Accuracy with units
  Add
2. Gap Ry Engineering Accuracy with units
  Add
Magnitude and direction Gap-fill
1. Gap $\theta$ Angle quantity 2020
  Add
2. Gap dir Choose one from a list
  Add
3. Gap ref Choose one from a list
  Add
4. Gap $R$ Engineering Accuracy with units
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

First, find the scalar components of the three forces.

$A_x =$ Ax $B_x =$ Bx $C_x =$ Cx

$A_y =$ Ay $B_y =$ By $C_y =$ Cy

Advice

Note: You an drag the vectors around to arrange them tip-to-tail. The resultant is a vector from the start of the chain to the end.

Vector Addition:

$R_x = \Sigma F_x = \simplify[!collectNumbers]{{scale FA[0]}+{scale FB[0]}+{scale FC[0]} ={scale FR[0]}}$ {units[1]}

$R_y = \Sigma F_y = \simplify[!collectNumbers]{{scale FA[1]}+{scale FB[1]}+{scale FC[1]} ={scale FR[1]}}$ {units[1]}

$R=\sqrt{R_x^2 + R_y^2} =\var{siground(resultant,4)}$

$\theta = \tan^{-1}\left(\left|\dfrac{R_y}{R_x}\right| \right) = \var{siground(theta,4)}$°

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Angle quantity 2020
Angle quantity 2020		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Engineering Accuracy with units
Engineering Accuracy with units		Hasn't run yet

This question is used in the following exams:

test by Chris King in Chris's workspace.
PRACTICE Vectors by Terry Young in NCDCS Unit 1 Intro to Matrices & Vectors.
Chapter 02 Exercises by Michael Proudman in Engineering Statics.
04. Vector Addition Rectangular Components by Michael Proudman in Engineering Statics.
vector new by abc temp in abc's workspace.
04. Vector Addition Rectangular Components by Sarah Sojka in Statics at Randolph College.
Andrew's copy of Chapter 2 Exercises by Andrew Burkert in Andrew's workspace.
Chapter 2 Exercises for studio 4 by Jay McCormack in 23-24 Studio 4 Statics Practice.
Algebra and Geometry by Deactivated user in Deactivated user's workspace.
Habeeba's copy of Chapter 2 Exercises by Habeeba Ahmed in Habeeba's workspace.
04. Vector Addition Rectangular Components by William Haynes in Engineering Statics.
Chapter 2 Exercises by William Haynes in Engineering Statics.
Ch. 2 Homework by Megan Voss in ENGR 212 Spring 2025.

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Vector addition by summing scalar components - easy

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Taxonomy: Kind of activity

Taxonomy: Context

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William Haynes 2 weeks, 6 days ago

William Haynes 1 month ago

William Haynes 1 year, 2 months ago

William Haynes 1 year, 2 months ago

William Haynes commented 1 year, 2 months ago

Jay McCormack 1 year, 7 months ago

William Haynes 2 years, 6 months ago

Jay McCormack 2 years, 6 months ago

Jay McCormack 2 years, 6 months ago

William Haynes 4 years, 2 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `vector`

Parts

Gap-fill

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Error

Vector addition by summing scalar components - easy

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 2 weeks, 6 days ago

William Haynes 1 month ago

William Haynes 1 year, 2 months ago

William Haynes 1 year, 2 months ago

William Haynes commented 1 year, 2 months ago

Jay McCormack 1 year, 7 months ago

William Haynes 2 years, 6 months ago

Jay McCormack 2 years, 6 months ago

Jay McCormack 2 years, 6 months ago

William Haynes 4 years, 2 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 4 years, 7 months ago

William Haynes 6 years, 6 months ago

William Haynes 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`