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How to Graph a Vector in GeoGebra

A vector in GeoGebra can be defined either by its coordinates, or by its start and end points.

GeoGebra Instruction 1

Defining Vectors

1.: Open Algebra View and Graphics View under View in Menu.
2.: If you know the coordinates of the vector, use the command Vector(<Point>) and enter the coordinates of the vector as a point—that is, as (x, y). If you only know the start and end points, use the command Vector(<Start Point>, <End Point>) and insert those values accordingly. Press Enter.
3.: The vector will be shown in Algebra View and Graphics View.

Screenshot of GeoGebra showing four vectors

You can work with vectors in the same way as numbers in GeoGebra. If the name of your object is a lowercase letter, then GeoGebra interprets the coordinates as a vector. Uppercase letter names are interpreted as points.

Example 1

If you have defined v:=(4, 3) and u:=(1, 3), then you can type 2v and get (8, 6), and u+v to get (5, 6).

You can also use GeoGebra to find the length of a vector.

GeoGebra Instruction 2

Length of a Vector

1.: Open Algebra View and Graphics View under View in Menu.
2.: Enter Length(<Object>), and fill in your vector for <Object>. Press Enter.
3.: The length is now shown as a separate number in Algebra View.

Screenshot of GeoGebra showing two points, a vector with its length

You can also use GeoGebra to find the distance between two points.

GeoGebra Instruction 3

Distance Between Points

1.: Open the side menu in the right corner.
2.: Under the View tab, select both Algebra View and Graphics View.
3.: Enter a point and an object (either a point or a vector) with appropriate names.
4.: Use the command Distance(<Point>, <Object>), fill in the names of the point and the object, and press Enter.
5.: The distance is now shown as a separate number in Algebra View.

Screenshot of GeoGebra showing two points, a vector with its length

The image above shows the distance between two points, $A$ and $B$ . It also shows the distance from the vector $\vec{u}$ and the point $A$ .

To find the distance between two points, you can either find the length of the vector going between them—as in Item 3—or use the command in Item 5.

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