Einführung in Vektoren

The motion of a ball through the air can be described using vectors—quantities that have both magnitude and direction.

In three-dimensional space, a vector is visualized as an arrow pointing from one point to another. The arrow's length represents the vector's magnitude, and its orientation shows direction

To describe a vector numerically, its displacement along each axis is captured using components. Components are numerical values written in angle brackets.

For example, a vector from the origin to the point (3, 2, 1) has components 〈3, 2, 1〉. This shows a displacement of three units along the x-axis, two units along the y-axis, and one unit upward along the z-axis. Since this vector starts at the origin, it is called a position vector.

When a vector connects two distinct points, A and B, its components represent the change in position. These components are found by subtracting the coordinates of A from those of B. These values show the net displacement along each axis.

Finally, the magnitude of a vector is its total length. It is calculated using the Pythagorean Theorem extended to three dimensions.