This applet should be useful in picking up vector addition and subtraction. You draw two vectors of your choice, choose the operation (Add or Subtract) and arrange the two vectors in a certain manner by dragging them. Drawing is done by pressing the mouse button at some point and dragging and releasing it at another point. If you watch the display you would see it updating giving the details of the vector that you are drawing. Once you have two vectors on the drawing space any one of them can be moved. Press the mouse button with cursor positioned on the dot at the midpoint of the vector and drag it. This will help you to reposition the vector parallel to itself.

The checkbox named reference causes reference lines and the angle made by the vector with x- axis to be displayed.

The vectors can be modified after drawing the two of them by using the cursor keys on the keyboard. Using the cursor keys with control key pressed will amplify the effect. The vector with a colored square at the mid point is  the selected vector for modification. By pressing on the dot at the midpoint of the other  vector the selection can be changed.

After the parallelogram or the triangle is formed you can drag the group of vectors. For this press and drag at any point other than the midpoints of the vectors. You can also double click to shift the location of the group of vectors.

Now for the manipulation:

To add, the vectors have to be arranged in order, that is with tail of one touching the tip of another. The sum vector is drawn by the applet if the you arrange the vectors so.

To subtract the vectors have to be arranged in improper order, that is, tips or tails of the two vectors should be made to touch. Again the applet draws the difference vector when the vectors are properly arranged.

Let me explain the subtraction part a bit. When you have A and B in improper order the vector joining the free ends is A - B or A depending on the direction. This vector is A - B, if it is in order with B and A, if it is in order with A. In the applet the vector A - B is being drawn. So this would be in order with B.

So draw away merrily and get a feel for the addition and subtraction of vectors.

Remember

To add - the vectors should be in order (tail of one touching the tip of another) and

To subtract - the vectors should be in improper order ( tails of the two vectors or tips of the two vectors should be touching each other)

Surendranath.B.