Vector equation of a line,

Error

There was an error loading the page.

Contributors

Feedback

From users who are not members of Content created by Newcastle University :

Bill Foster

said

Ready to use

6 years, 4 months ago

History

○

Bill Foster 6 years, 4 months ago

Gave some feedback: Ready to use

○

Newcastle University Mathematics and Statistics 9 years, 1 month ago

Created this.

Name	Status	Author	Last Modified
Vector equation of a line,	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Simon's copy of Vector equation of a line,	draft	Simon Thomas	01/04/2019 10:43

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

Question statement

You are given the vectors

$\begin{align} \boldsymbol{x_0} &= \var{vector(a,b,g)} , & \boldsymbol{v} & = \var{vector(c,d,f)}, \\[1em] \boldsymbol{y_0} &= \var{vector(a1,b1,g1)}, & \boldsymbol{w} &=\var{vector(c1,d1,f1)} \end{align}$

in $\mathbb{R^3}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-2
a1	integer	10
al	integer	2
b	integer	-6
b1	integer	-2
be	integer	4
c	integer	-3
c1	integer	2
d	integer	4
d1	integer	4
f	integer	8
f1	integer	-5
g	integer	-6
g1	integer	-37
ga	integer	-5
lam	integer	-2
mu	integer	-3
s1	integer	-1
s2	integer	-1
s3	integer	-1
s4	integer	1
v	matrix	matrix([-2,-6,-6])
w	matrix	matrix([-3,4,8])
p	vector	vector(4,-14,-22)

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`

-2

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Matrix entry
  Add
2. Gap Gap 1. Matrix entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Matrix entry
  Add
2. Gap Gap 1. Matrix entry
  Add
Part c) Gap-fill
1. Gap Matrix entry
  Add

Gap-fill

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

Find the vector equation of Line 1 which goes through the point $\boldsymbol{x_0}$ in the direction of the vector $\boldsymbol{v}$ .

Input the vector equation in the form:

$\boldsymbol{r} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix} + \lambda \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix}$

such that $\boldsymbol{r} = \boldsymbol{x_0}$ when $\lambda=0$ and $\boldsymbol{r}=\boldsymbol{x_0}+\boldsymbol{v}$ when $\lambda=1$ by filling in the appropriate fields below:

$\boldsymbol{r} =$ Gap 0. $+ \lambda$ Gap 1.

Advice

a)

$\boldsymbol{r} = \var{vector(a,b,g)} + \lambda \var{vector(c,d,f)}$

b)

$\boldsymbol{r} = \var{vector(a1,b1,g1)} + \mu \var{vector(c1,d1,f1)}$

c)

Write out a set of simultaneous equations for each component of $\boldsymbol{P}$ :

$\begin{align} \simplify[]{{a} + lambda*{c}} &= \simplify[]{{a1} + mu*{c1}} \\ \simplify[]{{b} + lambda*{d}} &= \simplify[]{{b1} + mu*{d1}} \\ \simplify[]{{g} + lambda*{f}} &= \simplify[]{{g1} + mu*{f1}} \end{align}$

By solving these equations, we find that the point $\boldsymbol{P}$ common to both lines is given by $\lambda=\var{lam},\mu=\var{mu}$ , and

$\boldsymbol{P} = \var{p}$

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
Matrix entry
Matrix entry		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Matrix entry
Matrix entry		Hasn't run yet

This question is used in the following exams:

Vectors by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
David's copy of Vectors by David Rickard in PHYS1010.
Eryk's copy of MATH6005 Vectors by Eryk Wilczy?ski in Eryk's workspace.
Maria's copy of Vectors by Maria Aneiros in Maria's workspace.
Vectors by Jeremie Wenger in Jeremie's workspace.
Newcastle U vector questions (3D points, lines and planes) by Jorj Kowszun in Jorj's workspace.
Nicolas's copy of Vectors by Nicolas Sawyer in Nicolas's workspace.
Maher's copy of Vectors by Maher Elbohouty in Vectors.
Quiz1 by Matt Falk in Matt's workspace.
Peter's copy of Vectors QUIZ by Peter Keys in Peter's workspace.
All the good stuff by Chris Templet in Chris's workspace.
Vectors by Angeliki Karperaki in Angeliki's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

Loading...

Error

Vector equation of a line,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`