MATH 2374 Lecture Notes - Lecture 1: Scalar Multiplication, Mathematical Object, Parallelogram
Document Summary
Vectors were in disguise in calc i and ii. A vector is a mathematical object with a direction and a magnitude (length) and direction, but no position. Also a vector is an element of a vector space. Think of a vector as being an arrow. Given an initial point a and a terminal point b, there is a vector ab (bolded or with a full or half arrow above the letters) If segment ab and segment cd are parallel, and |ab|=|cd|, then we should think of ab and cd as being the same vector. V, ab, cd are different representations of the same vector. The zero vector, written 0, is the vector of length 0 and no direction. To construct u+v, take representations of u and v where the initial parts coincide. Alternatively, u+v is the vector formed by the diagonal of the parallelogram, or by the tip to tail of both u and v.
