Selftest: Introduction to vector algebra

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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 $\vec{\mathbf{a}}$ 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 .

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