Learn Vectors through Animations

In this tutorial, I have included some GeoGebra animations for you to master vectors. You can interactively practise the following:

  • The nature of a column vector
  • Adding two vectors
  • Parallel Vectors
  • Vector equation of a line
  • The dot product or scalar product
  • The equation of a plane
  • The vector equation of a plane


Column Vectors

You can practise a column vectors in the following animation. Just move the vector and watch the values of the column vector.

The Sum of Two Vectors - vector addition

Move the two vectors to different points see how the sum of them changes.



Parallel Vectors

If two vectors are parallel, one vector can be expressed as a multiple of the other. Please move the slider to study it.



Vector Equation of a Line

The equation of a vector, r = a + λb, where a and b are a position vector of a fixed point and a direction vector respectively and λ is constant. 'r' is the position vector of an arbitrary point on the line.
Move the slider to change λ and observe the equation.




The Dot Product - Scalar Product

Please move the vectors and see how the dot product varies with the angle or the magnitudes of the vectors.




The Equation of a Plane

You may slightly move the grid to see the planes clearly.



The Vector Equation of a Plane

The vector equation of a plane, r.n = k, where k = a.n is illustrated here. 'a' is the position vector of the point, A. 'n' is the perpendicular vector.

Press the play button on the left to see the movement of the perpendicular vector, n.