Finding paths in vector diagrams
- It is important to be able to describe vectors by following paths through a geometric diagram
- The following grid is made up entirely of parallelograms, with the vectors and defined as marked in the diagram:
- It follows that:
- Keeping those things in mind, it is possible to describe any vector that goes from one point to another in the above diagram in terms of a and b
Adding and subtracting vectors follows all the same rules as adding and subtracting letters like x and y in algebra (this includes collecting like terms).
It doesn’t matter exactly what path you follow through a diagram from starting point to ending point – as long as you add and subtract the general vectors correctly along the path you use, you will get the correct answer.