Question

Why are they discussing vectors at the starting?

Answer 1

good as place as any to start. vectors are absolutely essential to the study of multi var calc. fundamentally important skills are usually done away with at the beginning of courses.

Answer 2

Vectors are an important simplified mental construct for extending the single variable systems we're used to dealing with to space in three dimensions or more. You could probably work through many of the problems without them but it would be tedious and prone to mistakes, not to mention a lot of work.

Answer 3

Vectors in space involve several variables, and by teaching vectors the teacher is able to introduce dot product, determinant and stuff.