Some of the content of this guide was modeled after a guide published by OpenStax and has been adapted for the NWP Learning Commons in January 2022. This work is licensed under a Creative Commons BY 4.0 International License.
When a physical unit is described by a single number, it is called a scalar quantity. When a direction is given to that scalar quantity, it becomes a vector.
The simplest vector to show and explain is displacement. An object moves from point A to point B. An overall distance travelled can be calculated with an appropriate direction given to the reference plane.
Parallel vectors can be added if they are in the same direction and subtracted if they are in opposite directions.
For the previous example, the vectors were in the same direction.
We will reverse the second vector and show why we subtract them:
When the problem moves beyond the linear plane into the 2-dimensional plane, the vectors can be combined by their individual x and y components to create a right-angle triangle.
Unit vectors are used to distinguish the direction and the magnitude of the overall vector.
Existing vectors can be rewritten as a combination of is and js. Treating these like variables, combine the like terms and what is left is a scalar quantity in the x direction denoted by i and a scalar quantity in the y direction denoted by j.
When combining vectors, add the i and j components separately to determine the new resultant vector.
When a vector is in the opposite direction (left in the x-axis and down in the y-axis), these are denoted as negative values. The combination of vectors is still denoted as addition but with the second vector having negative values it acts like subtraction.
