I'm given two vectors: F=9i+12j, V=3i+4j. I am asked to give the component of F parallel to V, the component of F perpendicular to V and the work done by force F through displacement V.
Well you can express F as:
Meaning that F is parallel to V.
Find the magnitude of F (using the Pythagoras' Theorem) this will be the parallel component.
The perpendicular component will be 0 since the two vectors are parallel.
Work Done = Force x Displacement.
Find the magnitude of the displacemnt V and you already have the force F, which is the parallel component of F to V.