Vectors: when perpendicular 1

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Bill Foster

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Bill Foster 55 years, 2 months ago

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Question statement

Given the vectors:

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
c	integer	-5
b	integer	-7
d	integer	2
g	integer	6
f	integer	10
s3	integer	-1
s2	integer	-1
s1	integer	1
s5	integer	1
s4	integer	1

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:

Statement
Advice
"Part a)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

Find $\lambda$ such that $\boldsymbol{A}$ and $\boldsymbol{B}$ are perpendicular to one another:

$\lambda =\;\;$ Unnamed gap.

Enter your answer as a fraction or an integer and not as a decimal.

Advice

a)

$\boldsymbol{A}$ and $\boldsymbol{B}$ are perpendicular to one another when $\boldsymbol{A \cdot B} = 0$ .

Now

$\begin{eqnarray*}\boldsymbol{A \cdot B} &=& \simplify[]{{a}*{c}+{b}*{d}+lambda*{f}}\\ &=& \simplify[std]{{f}*lambda+{a*c+b*d}} \end{eqnarray*}$
Hence

$\boldsymbol{A \cdot B} = 0 \Rightarrow \simplify[std]{{f}*lambda+{a*c+b*d}=0} \Rightarrow \lambda = \simplify[std]{{-a*c-b*d}/{f}}$

b)

$\boldsymbol{A}$ is in the $xy$ plane when $\lambda=0$ .

Give a worked solution to the whole question.

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

This question is used in the following exams:

Vectors 1 by Bill Foster in Bill's workspace.
Math6040 - Vectors by Julie Crowley in MATH6040 Technological Mathematics 201.
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Vectors 1A - scalar product by Ciara Fitzpatrick in Ciara's workspace.
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Maths Support: Dot and cross product by Anna Cartlidge in Glasgow Numbas Question Pool.
vectoren vragen inspiratie by abc temp in abc's workspace.
Jia's copy of mathcentre: Dot and cross product by Jia Shao in Jia's workspace.
Paul's copy of MATH6005 Vectors by Paul McFadden in Paul's workspace.
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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

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Error

Vectors: when perpendicular 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`