# Vector Definition

Description of the definition and drawing of different vectors

## Vectors

Vectors describe a direction and magnitude in a coordinate system. For calculations we use them as lists of numbers. But for understanding it can help to display them as geometric objects.

The vector $$\underline{x}=\left[\matrix{a\\b}\right]$$ has a magniutude $$|\underline{x}|=\sqrt{a^2+b^2}$$

A vector is uniquely determined by length, direction and orientation.

## Plot vectors

To draw a vector, use a coordinate system. Draw a horizontal line and a line perpendicular. The horizontal line is the X-axis; the vertical line is the Y-axis. The axes labeled with numbers for the scales of the corresponding units.

The following figure shows the vector $$\overrightarrow{a}=\left[\matrix{x\\y}\right]$$ or $$\overrightarrow{a}=\left[\matrix{2\\3}\right]$$

Die obere Zahl ist die x-Koordinate und die untere die y-Koordinate des Vektors.

Um den Vektor (2, 3) zu zeichen, ziehen Sie von einem Ausgangspunkt eine Linie 2 Einheiten auf der x-Achse nach rechts und 3 Einheiten auf der y-Achse nach oben

The vector is uniquely defined by its direction and its length.

## Equal Vectors

The following figure shows parallel vectors of equal length, direction and orientation. Since the location of a vector is arbitrary, these vectors are equal.

## Opposite Vectors

Parallel vectors of equal length but opposite in orientation are called opposite vector.

## Parallel Vectors

Two vectors are called in parallel if they have the same direction. They can be different lengths and have opposite orientations.