The world does revolve around us, we choose the coordinate system. We know how to handle stress and strain in a relationship. We have significant figures. If two bodies interact, their forces are equal and opposite. We can pull all-nighters.
Engineers do it to specifications.
We know the right hand rule. It's not the length of the vector that counts, it's how you apply the force. . . . . . . A priest, a drunkard and an engineer were condemned to die by the guillotine. The priest is led up to the guillotine and is asked if he prefers to be facing up or down. The executioner than fastens him in and releases the huge blade.