Difference between revisions of "Selftest: Introduction to vector algebra"

From Robotics
Jump to: navigation, search
 
(17 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
<quiz>
+
{{ExerciseNavigation|previous=[[Selftest: Cross product|Cross product]]|chapter=[[Vector algebra]]|article=[[Vector algebra]]|next=[[Selftest: Unit vector|Unit vector]]}}
 +
 
 +
<quiz display=simple>
 
{'''Difference between scalars and vectors'''
 
{'''Difference between scalars and vectors'''
  
Line 9: Line 11:
 
+A vector is defined by its magnitude and its direction.
 
+A vector is defined by its magnitude and its direction.
 
-All physical quantities are vectors.
 
-All physical quantities are vectors.
−
||Explanation: see [[Vector algebra]]
+
||Explanation: see [[Vector algebra|vector algebra]]
  
  
−
{'''Bedeutung von Vektoren'''
+
{'''Meaning of vectors'''
  
−
Bei welchen physikalischen Größen handelt es sich um vektorielle Größen?
+
Which of the following physical quantities are vectorial?
  
−
''(mehrere Antworten sind möglich)''}
+
''(multiple answers possible)''}
−
- Zeit
+
- Time
−
- Temperatur
+
- Temperature
−
+ Geschwindigkeit
+
+ Velocity
−
- Stromstärke
+
+ Acceleration
−
+ Beschleunigung
+
+ Force
−
+ Kraft
+
- Air preasure
−
+ Elektrische Feldstärke
+
||A vectorial quantity is directed, so its '''magnitude''' as well as its '''direction''' are necessary for its complete description (see [[Vector algebra|vector algebra]]).
−
- Luftdruck
 
−
||Es handelt sich genau dann um eine vektorielle Größe, wenn diese gerichtet ist, so dass zur vollständigen Beschreibung sowohl der '''Betrag''' als auch die '''Richtung''' erforderlich sind (vgl. [[Einführung in die Vektorrechnung]]).
 
  
  
 +
{ '''Magnitude and direction of vectors'''
  
−
{ '''Betrag und Richtung von Vektoren'''
+
Which of the following vectors have the same magnitude?
  
−
Welche der nachstehenden Vektoren sind betragsmäßig gleich?
+
''Fill in d, e or f in the following input fields.''
−
 
 
−
''Trage d, e oder f in die nachstehenden Felder ein.''
 
 
| type="{}" }
 
| type="{}" }
−
[[Bild:Vektorrechnung_Aufgabe3.svg|400px|Vektoren]]
+
[[File:vectoralgebra_selftest3.png|400px|Vectors]]
−
Vektor <math>\vec{\mathbf{a}}</math> und Vektor { f } sind betragsmäßig gleich.
+
Vector <math>\vec{\mathbf{a}}</math> and vector { f } have the same magnitude.
−
Vektor <math>\vec{\mathbf{b}}</math> und Vektor { e } sind betragsmäßig gleich.
+
Vector <math>\vec{\mathbf{b}}</math> and vector { e } have the same magnitude.
−
Vektor <math>\vec{\mathbf{c}}</math> und Vektor { d } sind betragsmäßig gleich.
+
Vector <math>\vec{\mathbf{c}}</math> and vector { d } have the same magnitude.
−
||Der Betrag des Vektors entspricht seiner Länge. Weitere Erklärungen: siehe [[Einführung in die Vektorrechnung]]
+
||The magnitude of a vector corresponds to its length. For further information see [[Vector algebra|vector algebra]].
  
  
  
  
−
{'''Ortsvektoren, freie und gebundene Vektoren'''
+
{'''Position, free and constrained vectors'''
  
−
Lückentext
+
Fill in the following words:
  
−
Fügen Sie die folgenden Wörter ein:
+
''free vector, constrained vector, position vector''
−
 
 
−
''freier Vektor, gebundenen Vektor, Ortsvektor''
 
  
 
| type="{}" }
 
| type="{}" }
−
Ein { freier Vektor } ändert seine Eigenschaften (Betrag und Richtung) nicht, wenn er parallel zu sich selbst derart verschoben wird, dass sein Anfangspunkt in einen beliebigen Raumpunkt fällt. Wenn die Eigenschaften eines Vektors an einen bestimmten Angriffspunkt gebunden sind, dann spricht man von einem { gebundenen Vektor }. Einen Vektor, der von einem festen Bezugspunkt auf einen bestimmten Punkt zeigt, bezeichnet man als { Ortsvektor }.
+
A { free vector } does not change its properties (magnitude and direction), if it is shifted parallel to itself so that its startpoint is translated to an arbitrary point in space. If the properties of a vector are constrained to a certain point, then it is a { constrained vector }. A vector pointing from a fixed origin to a certain point in space is called { position vector }.
 
</quiz>
 
</quiz>
 +
 +
[[Category:Selftest]]
 +
[[Category:Vectors]]

Latest revision as of 17:35, 30 January 2015

← Previous exercise: Cross product Exercises for chapter Vector algebra | Article: Vector algebra Next exercise: Unit vector →

1. Difference between scalars and vectors

Which statements are true?

(multiple answers possible)

A vector is defined by its magnitude.
A vector is defined by its direction.
A vector is defined by its magnitude and its direction.
All physical quantities are vectors.
→Explanation: see vector algebra

2. Meaning of vectors

Which of the following physical quantities are vectorial?

(multiple answers possible)

Time
Temperature
Velocity
Acceleration
Force
Air preasure
→A vectorial quantity is directed, so its magnitude as well as its direction are necessary for its complete description (see vector algebra).

3. Magnitude and direction of vectors

Which of the following vectors have the same magnitude?

Fill in d, e or f in the following input fields.

Vectors
Vector \vec{\mathbf{a}} and vector have the same magnitude.
Vector \vec{\mathbf{b}} and vector have the same magnitude.
Vector \vec{\mathbf{c}} and vector have the same magnitude.
→ The magnitude of a vector corresponds to its length. For further information see vector algebra.

4. Position, free and constrained vectors

Fill in the following words:

free vector, constrained vector, position vector

A does not change its properties (magnitude and direction), if it is shifted parallel to itself so that its startpoint is translated to an arbitrary point in space. If the properties of a vector are constrained to a certain point, then it is a . A vector pointing from a fixed origin to a certain point in space is called .

Your score is 0 / 0
Retrieved from "https://getwww.uni-paderborn.de/wiki/robotics/index.php?title=Selftest:_Introduction_to_vector_algebra&oldid=1402"