Simon's copy of 3d - angle between two vectors

Error

There was an error loading the page.

Contributors

History

○

Simon Thomas 5 years, 11 months ago

Created this as a copy of 3d - angle between two vectors.

Name	Status	Author	Last Modified
Vectors: inner or scalar product 1	draft	Bill Foster	06/08/2020 08:41
3d - angle between two vectors	Ready to use	Julie Crowley	07/10/2016 22:16
Violeta's copy of 3d - angle between two vectors	draft	Violeta CIT	17/01/2018 13:55
Simon's copy of 3d - angle between two vectors	draft	Simon Thomas	01/04/2019 10:03

There are 12 other versions that do you not have access to.

Question statement

Given the vectors:

$\boldsymbol{a}=\simplify[std]{{a}v:i+{b}v:j+{c}v:k},\;\;\;\boldsymbol{b}=\simplify[std]{{d}v:i+{f}v:j+{g}v:k}$

answer the following question:

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	2
c	integer	4
b	integer	6
d	integer	-5
g	integer	2
f	integer	2
s3	integer	1
s2	integer	1
s1	integer	1
s4	integer	-1
inner	integer	10
theta	number	76.5485666571

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
s1*random(2..9)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

→ Used by:

inner
theta

Statement
Advice
"Part a)" → "Unnamed gap" - Minimum accepted value
"Part a)" → "Unnamed gap" - Maximum accepted value
"Part b)" - Minimum accepted value
"Part b)" - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
1. Step Information only
Part b) Number entry
1. Step Information only

Gap-fill

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

Find $\boldsymbol{a\cdot b} =\;\;$ Unnamed gap

Advice

(a)

$\begin{eqnarray*} \boldsymbol{a\cdot b}&=& (\var{a}, \var{b},\var{c}) \cdot (\var{d}, \var{f},\var{g})\\ &=&({\var{a}\times\var{d})+(\var{b}\times\var{f})+(\var{c}\times\var{g})}\\ &=& \var{inner} \end{eqnarray*}$

(b)

$\mathbf{a}\cdot \mathbf{b}=|\mathbf{a}||\mathbf{b}|\cos\theta$ , where $\theta$ is the angle between the vector $\mathbf{a}$ and $\mathbf{b}$ .

Rearrange gives $\cos \theta =\frac{\mathbf{a}\cdot \mathbf{b}}{|\mathbf{a}||\mathbf{b}|}$

So for our question:

$\cos(\theta)=\left(\frac{\var{inner}}{\sqrt{(\var{a})^2+(\var{b})^2+(\var{c})^2}\sqrt{(\var{d})^2+(\var{f})^2+(\var{g})^2}}\right)$

$\cos(\theta)=\left(\frac{\var{inner}}{\sqrt{\var{a^2+b^2+c^2}}\sqrt{\var{d^2+f^2+g^2}}}\right)$

$\theta=\cos^{-1}\left(\frac{\var{inner}}{\sqrt{\var{a^2+b^2+c^2}}\sqrt{\var{d^2+f^2+g^2}}}\right)$

$\theta=\var{theta}$

which gives $\var{precround(theta,0)}$ to the nearest degree.

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
Number entry
Number entry		Hasn't run yet
Information only
Number entry
Number entry		Hasn't run yet
Information only

This question is used in the following exam:

Vectors by Simon Thomas in Maths support.

Loading...

Error

Simon's copy of 3d - angle between two vectors

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Simon's copy of 3d - angle between two vectors

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`