Selftest: Unit vector

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Exercises for chapter Vector algebra | Article: Unit vectors

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1. Which of the following figures shows a correct labeling?

Here you have to regard the correct labeling and assignment of the vector and the unit vector and also the magnitude of the unit vector.

→	Wrong:The magnitude of the vector is $\frac{1}{2}$. Unit vectors have a length of 1 (see unit vectors).
→	Correct:Here the unit vector has length 1 and both vectors point in the same direction.
→	Wrong:In this figure the labels of vector $\vec{\mathbf{a}}$ and the unit vector $\vec{\mathbf{e}}_a$ are interchanged. Hence the vector $\vec{\mathbf{a}}$ would always have length 1. But this is not generalizable. Furthermore a unit vector is not formed by multiplying the direction with a scalar, because it has always length 1. For further description please have a look at the article about unit vectors.
→	Correct:Here the unit vector has length 1 and both vectors point in the same direction.

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