Parallel vectors

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Julia Goedecke

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From users who are members of Linear Algebra 1st year :

Tatiana Tyukina	said	Ready to use	4 years, 7 months ago
Julia Goedecke	said	Needs to be tested	4 years, 7 months ago

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Tatiana Tyukina 4 years, 7 months ago

Gave some feedback: Ready to use

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Julia Goedecke 4 years, 7 months ago

Published this.

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Julia Goedecke 4 years, 7 months ago

Gave some feedback: Needs to be tested

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Julia Goedecke 4 years, 7 months ago

Created this.

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Question statement

This question is about parallel vectors in $\mathbb{R}^2$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

u	vector	vector(16,-1)
a	integer	4
b	integer	6
lambda	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector(lambda*a,-1)

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Description

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

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Generated value: `vector`

vector(16,-1)

← Depends on:

a
lambda

→ Used by:

Advice
"Part a)" - prompt
"Part b)" - prompt

Parts

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

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

For which value of $t$ , if any, is the vector $\begin{pmatrix}\var{a} \\ t^2\end{pmatrix}$ parallel to the vector $\var{u}$ ?

Enter NA if no such value exists. $t=$ Unnamed gap

Advice

Two vectors $u$ and $v$ are parallel if there is some scalar $\lambda$ such that $v=\lambda u$ (or the other way around).

a) To get $\begin{pmatrix}\var{a} \\ t^2\end{pmatrix}$ parallel to the vector $\var{u}$ , we would need $\lambda=\var{lambda}$ to make it work for the first entry. However, there is no (real number) $t$ such that $t^2=-\var{lambda}$ . So the answer is NA.

b) To get $\begin{pmatrix} \var{lambda}t \\ \var{b} \end{pmatrix}$ parallel to the vector $\var{u}$ , we need $\lambda = \var{-b}$ to make it work for the second entry:

$\begin{pmatrix}\var{lambda}t\\\var{b}\end{pmatrix}=\var{-b}\var{u}$

Then $t= \frac{\var{-b*lambda*a}}{\var{lambda}}=\var{-b*a}$ .

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Mathematical expression
Mathematical expression		Hasn't run yet
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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Tatiana Tyukina 4 years, 7 months ago

Julia Goedecke 4 years, 7 months ago

Julia Goedecke 4 years, 7 months ago

Julia Goedecke 4 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: `vector`

Parts

Gap-fill

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Parallel vectors

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Tatiana Tyukina 4 years, 7 months ago

Julia Goedecke 4 years, 7 months ago

Julia Goedecke 4 years, 7 months ago

Julia Goedecke 4 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`