Resolving a Vector Into Components

Resolving a Vector Into Components

In the examples from previous lessons, we have been adding vectors to determine the resultant vector. In many cases, however, we will need to do the opposite. We will need to take a single vector and find what other vectors added together produce it. In most cases, this involves determining the perpendicular components of a single vector, for example the x- and y- components, or the north-south and east-west components.

For example, we may know that the total displacement of a person walking in a city is 10.3 blocks in a direction \(\text{29}\text{.0º}\) north of east and want to find out how many blocks east and north had to be walked.

This method is called finding the components (or parts) of the displacement in the east and north directions, and it is the inverse of the process followed to find the total displacement. It is one example of finding the components of a vector.

There are many applications in physics where this is a useful thing to do. We will see this soon when looking at projectile motion, and much more when we cover forces in another tutorial. Most of these involve finding components along perpendicular axes (such as north and east), so that right triangles are involved. The analytical techniques presented in the next couple of lessons are ideal for finding vector components.