Sorry, enough years of only math/physics can give one a disconnect. I'm not trying to be condescending, only trying to get you out of the 'everything is a formula' mode. In highschool, I too used the same everything is described through formulas mode, and I know in hindsight I should have been taught or told otherwise. I know that at one point I too was still trying to get the idea of vectors straight, and it's only because I've worked with them day in and day out that their form becomes second nature.
I could for example, define an angle from the y-axis to a vector. Say, for illustrative purposes, that the vector is 3x+4y. If I define an angle to be between the y axis and the vector then the angle is given by arctan(3/4). Similarly, still defining the angle to be with respect to the y axis, if the vector was 0x+4y, then arctan(0/4) gives Ø=0. So in this definition of angle it makes sense to say that a vector that 4y+0x has an angle of 0, i.e. the vector is on the axis that defines the angle.