Angle between two vectors

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Julie Crowley

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Julie Crowley 11 years ago

Created this as a copy of tg_Vinkel mellom vektorer.

Name	Status	Author	Last Modified
Angle between two vectors	draft	Julie Crowley	26/07/2016 12:51
Angle between two vectors	draft	Marie Nicholson	08/11/2018 12:29

There are 4 other versions that do you not have access to.

Question statement

Given the vectors
$\mathbf{A}=\var{fa}\mathbf{i}+\var{sa}\mathbf{j}+\var{ta}\mathbf{k},\;\;\;\boldsymbol{B}=\var{fb}\mathbf{i}+\var{sb}\mathbf{j}+ \var{tb}\mathbf{k}$

Find the angle between these vectors in degrees and radians.

Note that the angle must be between $0\,^{\circ}$ and $180\,^{\circ}$ (between $0$ and $\pi$ radians)

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
c	integer	1
b	integer	2
angle	number	60.0
d	integer	3
g	integer	1
s3	integer	-1
s2	integer	-1
s1	integer	-1
s4	integer	1
fa	integer	-1
fb	integer	-1
u	integer	2
t	integer	3
sb	integer	0
sa	integer	-1
tb	integer	1
ta	integer	0

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
if(t=1,2,1)

JME function reference

Description

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

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Generated value: `integer`

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Mathematical expression
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Gap-fill

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

Angle in degrees = Gap 0. $^{\circ}$

Angle in radians = Gap 1.radians.

Note that you can input the radians as a decimal to 4 decimal places or as a mulptiple of $\pi$ . You input $\pi$ as pi.

Advice

Bruker formelen:

$\boldsymbol{A \cdot B} = |\boldsymbol{A}||\boldsymbol{B}|\cos(\theta)$ der $\theta$ er vinkelen mellom vektorene.

Her er $|\boldsymbol{A}| = \sqrt{ (\var{s1})^2+(\var{s2})^2} = \simplify[all]{sqrt({s1^2+s2^2})},\;\;\;|\boldsymbol{B}| = \sqrt{ (\var{s3})^2+(\var{s4})^2} = \simplify[all]{sqrt({s3^2+s4^2})}$

$\boldsymbol{A \cdot B} = (\var{fa},\var{sa}, \var{ta}) \cdot (\var{fb},\var{sb}, \var{tb}) = \var{g}$ .

Slik at

$\begin{eqnarray*} \cos(\theta)&=&\frac{\var{g}}{\sqrt{2}\sqrt{2}} = \simplify[std]{{g}/{2}}\\ \Rightarrow \theta &=&\arccos\left(\simplify[std]{{g}/{2}}\right)\\ &=&\var{angle}\,^{\circ} \end{eqnarray*}$
Konvertering fra grader til radianer gjøres ved å multiplisere vinkel i grader med

$\displaystyle \frac{\pi}{180}$ .

Da blir $\displaystyle \var{angle}\,^{\circ}=\simplify[std]{({angle}*pi)/{180}= {precround(angle*pi/180,4)}}$ radianer i 4 siffers nøyaktighet.

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This question is used in the following exams:

MATH6005 Vectors by Julie Crowley in MATH6005 Engineering Mathematics 101.
Stephen's copy of MATH6005 Vectors by Stephen Bowlzer in Stephen's workspace.
Gareth's copy of MATH6005 Vectors by Gareth Woods in Gareth's workspace.
MATH6005 Vectors by Michael Proudman in .Vectors.
MATH6005 Vectors by Violeta CIT in MATH6005 Engineering Mathematics 101.
Vectors 4 by Marie Nicholson in MATH 6005 2018_2019.
Paul's copy of MATH6005 Vectors by Paul McFadden in Paul's workspace.
All the good stuff by Chris Templet in Chris's workspace.
Inna's copy of MATH6005 Vectors by Inna Namestnikova in Inna's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

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Julie Crowley 11 years ago

Error in variable testing condition

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Generated value: `integer`

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Angle between two vectors

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Julie Crowley 11 years ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`