Vector Addition and Scalar Multiplication

This applet investigates addition and scalar multiplication of 2D column vectors and represents this on a plane with a rectangular or vector (parallelogram) grid.

Author and programmer: Ron Barrow

UK Years 10-13, KS4, KS5, Higher GCSE Mathematics, AS - Shape and Space, Investigative tools


Instructions below

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How to Use this Applet

On the screen you will see two vectors represented. Vector a is represented by the blue line and circle, while vector b is represented by the green line and circle. The lines are drawn from the origin (the black dot) to the heads of the vectors, where you see the little circles. The values of the vectors are calculated and written on the right of the screen.
You can move the vectors around by clicking the small blue and green circles and dragging with your mouse. Notice how the values of the vectors relate to the coordinates.
The sliders at the bottom enable you to multiply the vectors by fixed numbers from -5 to 5. The left (blue) one, labelled "r", multiplies vector a, while the right (green) one, labelled "s", multiplies vector b.

The third line on the grid represents the effect of adding the vectors, or multiples of them. This new vector is equal to: ra + sb, where r and s are the multiplying numbers obtained from the two sliders at the bottom. Its value is calculated and displayed in white on the right of the screen. By studying this you should get an idea of how vectors are added. Checking the box "Complete parallegram" adds some lines to show geometrically what is going on.
You can change the background grid to a vector grid by clicking "Vector Grid", where the gridlines depend on the vectors thenselves. Notice that these gridlines change as you move the vectors. Try it! You can also have no grid at all (click "No grid").
Vectors are very important in maths and science, and this applet is designed to introduce you to the way they behave. Play around!