How to Compute Scalar Products of Vectors with GeoGebra

There are commands in GeoGebra to find both scalar products and angles between vectors. Note that GeoGebra uses the term dot product for the scalar product.

GeoGebra Instruction 1

Scalar Product

1.: Open CAS in View-menu.
2.: Enter

Dot(<Vector>, <Vector>)

in CAS, and fill in the coordinates of the vectors—or their names—to find the scalar product of them. Press Enter.
3.: You can also write the scalar product as a multiplication using * in CAS.

Screenshot of GeoGebra showing the dot product of two vectors

Below, we’ll look at how to use GeoGebra to find angles. Keep in mind that CAS by default is set to return the answer in radians, not degrees!

Then, in the final item of the instructions below, we’ll review how to convert the answer into degrees.

GeoGebra Instruction 2

Angle

1.: Open CAS under View in Menu.
2.: Enter

Angle(<Vector>, <Vector>)

and fill in the coordinates of the vectors—or their names—that you want to find the angle between. Press Enter.
3.: If you now get a strange expression (typically containing atan, acos or asin), select the expression by clicking on it, and then click the button Numeric Evaluation .
4.: If the answer does not contain a degree symbol (and is probably a relatively low number), it is given in radians. To convert it to degrees, divide the answer by the $^{\circ}$ symbol (alt+o) or the string deg. Here, deg is short for degree. You will now get your answer in degrees.

Screenshot of GeoGebra showing the angle between to vectors

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