Angle between two vectors

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Marie Nicholson 6 years, 4 months ago

Created this as a copy of Angle between two vectors.

Name	Status	Author	Last Modified
Angle between two vectors	draft	Julie Crowley	26/07/2016 12:51
Angle between two vectors	draft	Marie Nicholson	08/11/2018 12:29

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Question statement

Given the vectors
$\mathbf{a}=\var{fa}\mathbf{i}+\var{sa}\mathbf{j}+\var{ta}\mathbf{k},\;\;\;\mathbf{b}=\var{fb}\mathbf{i}+\var{sb}\mathbf{j}+ \var{tb}\mathbf{k}$

Find the angle between these vectors in degrees and radians.

Note that the angle must be between $0\,^{\circ}$ and $180\,^{\circ}$ (between $0$ and $\pi$ radians)

Give any introductory information the student needs.

			Name	Type	Generated Value

s1	integer	1
a	integer	1
s4	integer	1
fa	integer	1
angle	number	120.0
g	integer	-1
fb	integer	-1
tb	integer	1
sb	integer	0
ta	integer	0
c	integer	1
sa	integer	1
s2	integer	1
s3	integer	-1
u	integer	2
d	integer	3
b	integer	2
t	integer	3

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random(1,-1)

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Description

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Generated value: `integer`

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. Mathematical expression
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Gap-fill

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Angle in degrees = Gap 0. $^{\circ}$

Angle in radians = Gap 1.radians.

Note that you can input the radians as a decimal to 4 decimal places or as a mulptiple of $\pi$ . You input $\pi$ as pi.

Advice

Bruker formelen:

$\boldsymbol{A \cdot B} = |\boldsymbol{A}||\boldsymbol{B}|\cos(\theta)$ der $\theta$ er vinkelen mellom vektorene.

Her er $|\boldsymbol{A}| = \sqrt{ (\var{s1})^2+(\var{s2})^2} = \simplify[all]{sqrt({s1^2+s2^2})},\;\;\;|\boldsymbol{B}| = \sqrt{ (\var{s3})^2+(\var{s4})^2} = \simplify[all]{sqrt({s3^2+s4^2})}$

$\boldsymbol{A \cdot B} = (\var{fa},\var{sa}, \var{ta}) \cdot (\var{fb},\var{sb}, \var{tb}) = \var{g}$ .

Slik at $\begin{eqnarray*} \cos(\theta)&=&\frac{\var{g}}{\sqrt{2}\sqrt{2}} = \simplify[std]{{g}/{2}}\\ \Rightarrow \theta &=&\arccos\left(\simplify[std]{{g}/{2}}\right)\\ &=&\var{angle}\,^{\circ} \end{eqnarray*}$
Konvertering fra grader til radianer gjøres ved å multiplisere vinkel i grader med $\displaystyle \frac{\pi}{180}$ .

Da blir $\displaystyle \var{angle}\,^{\circ}=\simplify[std]{({angle}*pi)/{180}= {precround(angle*pi/180,4)}}$ radianer i 4 siffers nøyaktighet.

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This question is used in the following exam:

Vectors - Ex. Sheet 2 by Marie Nicholson in MATH 6005 2018_2019.

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Marie Nicholson 6 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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Angle between two vectors

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Marie Nicholson 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`