I understand how to work with vectors but I am not yet very confident on how they work or think about them. I am working with mechanics A level. For example how would you imagine the velocity vector (2i +5j) m/s. So I am assuming that the object is moving at 2m/s east or along the x-axis and 5m/s along the y-axis or north. Am I right? So suppose an object is moving in a direction [tex]3i-4j[/tex] and has speed 10m/s. Could you explain how finding the velocity in that direction works. I know how to work it out but not exactly how to think about it. I know I would find the magnitude of [tex]3i-4j[/tex] which is; [tex]√(3^2+4^2)[/tex] then; Velocity is equal to: [tex]10χ1/5(3i-4j) = (6i-8j)[/tex] I have trained myself to work that out but I am not sure about the logic behind it. Please explain. More bout vectors in general. Thank you.