Sketching Tail-to-Tail Method

Sketching Tail-to-Tail Method

In this method we draw the two vectors with their tails on the origin. Then we draw a line parallel to the first vector from the head of the second vector and vice versa. Where the parallel lines intersect is the head of the resultant vector that will also start at the origin. We will only deal with perpendicular vectors but this procedure works for any vectors.

Let us apply this procedure to the same two vectors we used to illustrate the head-to-tail method:

• \(\vec{F}_{1} = \text{2}\text{ N}\) in the positive \(y\)-direction
• \(\vec{F}_{2} = \text{1.5}\text{ N}\) in the positive \(x\)-direction

We first draw a Cartesian plane with the first vector originating at the origin:

Then we add the second vector but also originating from the origin so that the vectors are drawn tail-to-tail:

Now we draw a line parallel to \(\vec{F}_{1}\) from the head of \(\vec{F}_{2}\):

Next we draw a line parallel to \(\vec{F}_{2}\) from the head of \(\vec{F}_{1}\):

Where the two lines intersect is the head of the resultant vector which will originate at the origin so:

You might be asking what you would do if you had more than 2 vectors to add together. In this case all you need to do is first determine \(\vec{R}_{x}\) by adding all the vectors that are parallel to the \(x\)-direction and \(\vec{R}_{y}\) by adding all the vectors that are parallel to the \(y\)-direction. Then you use the tail-to-tail method to find the resultant of \(\vec{R}_{x}\) and \(\vec{R}_{y}\).