Vectors Definition 1. A vector is formally defined as an element of a vector space In the commonly encountered vector space R (i.e., Euclidean n-space), a vector is given by n components and can be specified as (vi, v2, -. , Un) Vectors are sometimes referred to by the number of coordinates that they have. So a 2-dimensional vector (ui, u2) is often called a two-vector and a 3-dimensional vector (u1,u2, ua) is called a three-vector. More generally, an n-dimensional vector is often called an n-vector Vectors can be added together (vector addition), subtracted (vector subtrac- tion) and multiplied by scalars (scalar multiplication). Vector multiplication is not uniquely defined, but a number of different types of products, such as the dot product and cross product are commonly defined for vectors Operations on Vectors Definition 2. Addition/Subtraction: These operations are binary op- erations on vectors. Two vector can the same dimension, number of coordinates. When adding or subtracting two vectors, add or subtract corresponding coordinates ded or subtracted only if they have Vectors Definition 1. A vector is formally defined as an element of a vector space In the commonly encountered vector space R (i.e., Euclidean n-space), a vector is given by n components and can be specified as (vi, v2, -. , Un) Vectors are sometimes referred to by the number of coordinates that they have. So a 2-dimensional vector (ui, u2) is often called a two-vector and a 3-dimensional vector (u1,u2, ua) is called a three-vector. More generally, an n-dimensional vector is often called an n-vector Vectors can be added together (vector addition), subtracted (vector subtrac- tion) and multiplied by scalars (scalar multiplication). Vector multiplication is not uniquely defined, but a number of different types of products, such as the dot product and cross product are commonly defined for vectors Operations on Vectors Definition 2. Addition/Subtraction: These operations are binary op- erations on vectors. Two vector can the same dimension, number of coordinates. When adding or subtracting two vectors, add or subtract corresponding coordinates ded or subtracted only if they have