Projections
If you have two vectors it can be helpful to find out how far one is "projecting" on to the other. See Examples for a more in-depth explanation.
There are two main projections:
- vector projection
- scalar component
A vector projection is the vector of the projection, given by the following equation:
A scalar component if the scalar of the projection, given by the following equation:
Examples
Ex. 1
Imagine that you are driving a car driving south and you take a left turn going east. Your complete movement, shown by the blue line below, is made up of the distance you moved south and the distance you moved east.
The projection of your turn on the west-east axis (aka x-axis) is shown by the green line, and the projection of your turn on the north-south axis (aka y-axis) is shown by the yellow line.
Ex. 2
Imagine you have a vector and a flashlight, you hold the flashlight parallel to the x-axis and shine your flashlight on the vector (blue). The length of the shadow would be the vector's projection (purple) on the y-axis (roughly, you have to ignore the shadow's elongation).
