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How to Check If Two Vectors are Parallel Using GeoGebra

There are two ways to find out if two vectors are parallel in GeoGebra. One is simply to solve the vector equation $\vec{a} = k \cdot \vec{b}$ in CAS. The other is to draw two lines and use a GeoGebra command to check if they are parallel.

GeoGebra Instruction 1

Method 1

1.: Open Algebra View and Graphics View under View in Menu.
2.: Enter your two vectors in Algebra View.
3.: Enter

<first vector> = k * <second vector>

in CAS. Be sure to fill in your vectors with the names they are given in Algebra View. Click Solve .
4.: If you get a solution for $k$ , the vectors are parallel. If you get ${}$ , the vectors are not parallel.

Screenshot of GeoGebra showing two parallel vectors

GeoGebra Instruction 2

Method 2

1.

Open Algebra View and Graphics View in

View menu.

2.

Define your two vectors in Algebra View.

3.

Enter

Line(<point>, <direction vector>)

in Input Bar. Fill in (0,0) for <point> and one of the vectors for <direction vector>. Press Enter. The line should now be shown Algebra View and Graphics View.

4.

Repeat the above method for your other vector as well.

5.

Enter

AreParallel(<line>, <line>)

in Algebra View. Input your two lines into the fields and press Enter. If true is displayed in Algebra View, the vectors are parallel. If false is displayed in Algebra View, the vectors are not parallel.

Screenshot of GeoGebra showing two lines and the output "false"

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