I've not had linear algebra yet, so bear with me if I write something weird. Given vector A and B as shown above, how do I transform vector B so that one of its components is parallel to A, and the other perpendicular?
The application is as follows: Vector A represents the direction of an object, vector B represents an acceleration. I want to find out the acceleration that points in the object's direction, (its tangential acceleration), and the acceleration pointing perpendicular to the object (radial acceleration).
Hint:
Use the dot product between two vectors to get the parallel components by using the following formula $$\overrightarrow{B}.\frac{\overrightarrow{A}}{|A|}$$
For perpendicular component, you can get another vector perpendicular to $\overrightarrow{A}$ and use the same fromula.