When I teach about vectors, I find that I often have to pull from a few different sources. Some methods for solving vectors such as using Trig functions and the Pythagorean theorem are found directly in regents review books, but in order to elevate my students' knowledge of vectors, I want them to be able to solve for the resultant of more than just two vectors at a time. Also, vectors at right angles to each other isn't much of a challenge is it?
I remember being troubled at how much trigonometry my students would have to do to solve for the resultant vector of three components until I found another resource from CPO science that solved vectors graphically. The resultant was solved simply by adding up the x-components and adding up the y-components and then from there using Pythagorean theorem. The x- and y-components were simply the (x,y) coordinates of the vector. Now my students can solve for the resultant of four vectors, five vectors, six vectors, etc.
As for the other extreme, there are also simpler ways of solving for vectors such as the Parallelogram Rule. I think I might have first heard this one from Paul G. Hewitt, the author of Conceptual Physics. This one uses only two component vectors. You create a parallelogram and then, depending on where the arrow heads point, connect corner to corner. This method is really more for the beginning stages of learning about vectors.
The last one, is one that can be simple or complicated depending on how the student sees it. The last way to solve for vectors is by using a scale. The regents review books don't out right teach this, but they give problems where students are asked to calculate the scale, use a ruler to measure the vector, and then using their scale to calculate another component of the vectors.
This handbook is a concise summary of all five of these methods. Plus, it's illustrated :)
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