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You can use GeoGebra to solve vector equations. You can solve them by using systems of equations, or by using the vectors, if you know the coordinates. There is also a separate entry about solving systems of equations with GeoGebra .
GeoGebra Instruction 1
CAS and Graphics View in View menu. CAS. It is wise to define your vectors using lowercase letters (for example u:=(1,2) and v:=(3,4)). This is because GeoGebra interprets your input as a point, not as a vector, if you use capital letters! Solutions(<equation>) in CAS, where you replace <equation> with your equation. You also need to type the variables you wish to solve in respect to.