# Selftest: Introduction to vector algebra

From Robotics

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Exercises for chapter Vector algebra | Article: Vector algebra |
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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.*

Vector and vector |

Vector and vector |

Vector and vector |

→ 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 |