Graphical Vector Addition and Subtraction

Consider two vectors and , as shown in the figure on the right. Let us see how we can add and subtract them graphically. The first thing we would like you to notice is that a vector is only specified by its length and angle relative to the x-axis. So even though we have drawn both of these vectors to be originating at the point x=0, y=0, this is not necessary. Vectors can be moved around in space in an arbitrary fashion. As long as you do not change their length and angle relative to the x-axis, the vectors remain unchanged by these translational operations. This is why we leave away the coordinate system now.

Vector addition:

• We put the tail of on the head of , or the other way around, to get = + = + .

  now has the right length and angle with respect to x-axis.

Vector subtraction:

• (Here the order matters: - is not equal to - )
  1. Reverse the direction of to create a vector - = +(- )

     then add to - by the head to tail method

  2. - : This vector can be constructed just like - but the vector you want to reverse is .

© MultiMedia Physics, 1999