Harry's copy of Find unit vector parallel to given vector,

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Harry Flynn

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Harry Flynn 7 years, 1 month ago

Created this as a copy of Find unit vector parallel to given vector, .

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(6,-1,-5)
lenu	number	7.874007874
unitu	vector	vector(0.762,-0.127,-0.635)

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(6,-1,-5)

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
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 $-\boldsymbol{\hat{u}}=\pmatrix{\var{-unitu[0]},\var{-unitu[1]},\var{-unitu[2]}}$ .

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Harry's copy of Find unit vector parallel to given vector,

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Taxonomy: mathcentre

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Harry Flynn 7 years, 1 month ago

Error in variable testing condition

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Generated value: `vector`

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Harry's copy of Find unit vector parallel to given vector,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Harry Flynn 7 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: vector

Parts

Gap-fill

Generated value: `vector`