Measures of motion (displacement, velocity, acceleration) and forces are all vectors so any study involving these would require vector calculus.
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Hence the reason for why it is called Vector Calculus, Vector Calc. is simply an expansion in the calculus subject are in math. It deals with Taylor's Formula (in calc 2 you learn the taylor polynomial and the taylor series), theorems from Green, Gauss, and Stokes, and much more.
Vector calculus is applied in electrical engineering especially with the use of electromagnetics. It is also applied in fluid dynamics, as well as statics.
Mechanical engineering usually deals with forces and their effects on materials. Forces are vectors and so, to study their effects you need to use vector calculus.
A vector whose direction (angles) and line of application are fixed, but whose point of application is not fixed.
One uses calculus including differential equations and vector calculus in the undergrad courses which is as far as got.