Blind students should be able to do a pretty good job of adding two vectors with thismethod using a graph board, some pushpins, and five pipe cleaners. Try to
keep the pipe cleaners as straight as practical. Consider making a loop at eachend of four of the pipe cleaners that you can use to pin them down to the graph board.
Given two vectors...
Given two vectors A and B, which are specified in terms of the magnitude of each vector and the
angle that each vector makes relative to the horizontal axis, follow these steps:
- Cut or bend two pipe cleaners to the correct length for one of the
vectors. Set one aside temporarily.
- Cut or bent two pipe cleaners to the correct length for the other
vector. Set one aside temporarily.
- Position two of the pipe cleaners so as to represent the pair of
vectors connected at their tails with the correct angle between them. (Make each vector form the correct angle relative tothe horizontal axis.) Pin each end of each vector down to hold it at the correct
location with the correct angle. Think of the point wheretheir tails join as the origin of a Cartesian coordinate system.
- Use the other two pipe cleaners to form a parallelogram. Pin the ends of
those pipe cleaners down using the pushpins at the ends of the vectors plus one additional pushpin. If you pin the ends of those two pipecleaners to the ends of the vectors first, you should be able to find the
point where those two pipe cleaners meet and pin them down at that point.That will be the "opposite corner" of the parallelogram. If you end up with
a four-sided geometric shape that is not a parallelogram, you have used thefinal two pipe cleaners in the wrong order. Switch them and draw the
parallelogram again.
- Place a fifth pipe cleaner from the origin to the opposite corner of the
parallelogram. The length of that vector will be the magnitude of the sum ofthe other two vectors. The angle that vector forms with the horizontal axis will
be the angle of the sum of the other two vectors.
Angles,
approaches, and vector naming convention
Make one vector horizontal
In order to make the computations and the manipulations of the pipe cleaners in the following
examples easier, I will cause one of the two vectors to lie on thehorizontal axis with an angle of 0 degrees. That won't make the results any less
general, but it will make it easier for you to get accurate results.
The parallelogram method
I may be wrong, but I believe that the parallelogram method for adding two
vector is more practical for blind students than the tail-to-tip method.Therefore, I will walk you through a parallelogram solution and a trigonometry
solution for several of the example scenarios.
Vector naming convention
I will define vectors in the following way:
- Bm = 10 units
- Ba = 45 degrees
- Cs = B + A
- Cd = B - A
where
- Bm is the magnitude of a vector named B.
- Ba is the angle that the vector named B makes with the horizontal axis.
- Cs and Cd are the sum and difference of two vectors respectively.
- Csm and Cdm are the magnitudes of the sum and difference of two vectors.
- Csa and Cda are the angles (relative to the horizontal axis) of the sum
and difference of two vectors.
