Find unit vector parallel to given vector,

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Bill Foster

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Has some problems

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Bill Foster 6 years, 6 months ago

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Name	Status	Author	Last Modified
Find unit vector parallel to given vector,	Has some problems	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Harry's copy of Find unit vector parallel to given vector,	draft	Harry Flynn	09/03/2018 14:33

Question statement

Find a unit vector $\boldsymbol{\hat{a}}$ , which is parallel to $\boldsymbol{u}=\pmatrix{\var{u[0]},\var{u[1]},\var{u[2]}}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

u	vector	vector(2,-2,-5)
lenu	number	5.7445626465
unitu	vector	vector(0.348,-0.348,-0.870)

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
vector(repeat(random(1..9)*sign(random(1,-1)),3))

JME function reference

Description

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

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Generated value: `vector`

vector(2,-2,-5)

→ Used by:

lenu
unitu

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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Ask the student a question, and give any hints about how they should answer this part.

$\boldsymbol{\hat{a}}=($ Gap 0. $,$ Gap 1. $,$ Gap 2. $)$ . (Enter your answers to 3d.p.)

Advice

Note that in this advice, the full calculator display is used in the calculation of each step; any rounding is purely for display clarity.

There is only one unit vector parallel to a vector $\boldsymbol{u}=\pmatrix{u_1,u_2,u_3}$ , namely the unit vector $\boldsymbol{\hat{u}}=\boldsymbol{u}/\lvert\boldsymbol{u}\rvert$ , where $\lvert\boldsymbol{u}\rvert=\sqrt{u_1^2+u_2^2+u_3^2}$ .

In this question $\lvert\boldsymbol{u}\rvert=\sqrt{(\var{u[0]})^2+(\var{u[1]})^2+(\var{u[2]})^2}=\var{precround(lenu,3)}$ , and so $\boldsymbol{\hat{a}}=\boldsymbol{\hat{u}}=\frac{1}{\var{precround(lenu,3)}}\pmatrix{\var{u[0]},\var{u[1]},\var{u[2]}}=\pmatrix{\var{unitu[0]},\var{unitu[1]},\var{unitu[2]}}$ to 3d.p.

There is also an anti-parallel unit vector $-\boldsymbol{\hat{u}}=\pmatrix{\var{-unitu[0]},\var{-unitu[1]},\var{-unitu[2]}}$ .

Give a worked solution to the whole question.

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This question is used in the following exams:

Vector calculus by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
Jorj's copy of Vector calculus by Jorj Kowszun in Jorj's workspace.
Alvaro's copy of Vector calculus by Alvaro Martínez in Alvaro's workspace.
Vector calculus by steve kilgallon in Vector Calculus.
Vector calculus exam by Simon Thomas in Vector calculus.
Nicolas's copy of Vector calculus by Nicolas Sawyer in Nicolas's workspace.
Vector calculus by Michael Proudman in .Vectors.
Vector calculus by steve kilgallon in Vectors.

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Bill Foster 6 years, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `vector`

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Find unit vector parallel to given vector,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`