Vectors: cross product 1

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Bill Foster

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Bill Foster 55 years, 4 months ago

Created this.

Name	Status	Author	Last Modified
Vectors: cross product 1	draft	Bill Foster	06/08/2020 08:41
Cross product 1	Ready to use	Julie Crowley	07/10/2016 22:15
Cross product	draft	Marie Nicholson	08/11/2018 12:33
Cross product	draft	Clodagh Carroll	14/11/2018 17:08
Clodagh's copy of Cross product	draft	Clodagh Carroll	14/11/2018 17:17
Simon's copy of Cross product 1	draft	Simon Thomas	01/04/2019 10:21

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Question statement

Given the vectors:

$\boldsymbol{A}=\simplify[std]{{a}v:e_1+{b}v:e_2+{g}v:e_3},\;\;\;\boldsymbol{B}=\simplify[std]{{c}v:e_1+{d}v:e_2+{f}v:e_3}$

answer the following question:

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-4
c	integer	-4
b	integer	7
d	integer	4
g	integer	-5
f	integer	2
s3	integer	-1
s2	integer	1
s1	integer	-1
s5	integer	1
s4	integer	1
inner	integer	34

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`

-4

← 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. Number entry
  Add
3. Gap Gap 2. Number entry
  Add

Gap-fill

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

Find $\boldsymbol{A\times B} =$ Gap 0. $\boldsymbol{e_1} + \;$ Gap 1. $\boldsymbol{e_2} + \;$ Gap 2. $\boldsymbol{e_3}$

Advice

$\begin{eqnarray*} \boldsymbol{A\times B}&=& \begin{vmatrix} \boldsymbol{e_1} & \boldsymbol{e_2} &\boldsymbol{e_3}\\ \var{a} & \var{b} & \var{g}\\ \var{c} & \var{d} & \var{f} \end{vmatrix}\\ \\ &=&\simplify[]{({b}*{f}-{g}*{d})v:e_1 + ({g}*{c} - {a}*{f})v:e_2+({a}*{d}-{b}*{c})v:e_3}\\ \\ &=&\simplify[std]{{b*f-g*d}v:e_1+{g*c-a*f}v:e_2+{a*d-b*c}v:e_3} \end{eqnarray*}$

Give a worked solution to the whole question.

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Bill Foster 55 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Vectors: cross product 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`