Here are some examples of how to create Arrays:

//This is an array:
var arr:Array = [];

//So is this:
var arr:Array = new Array();

//This is a predetermined length array:
var arr:Array = new Array(5); //Sets to 5 elements (each are null)

And here’s how to create vectors:

//Create a vector that will only accept strings:
var vec:Vector.<String> = new Vector.<String>();

//This initiates the vector to a predetermined length:
//Creates 5 null elements;
var vec:Vector.<String> = new Vector.<String>(5); `

//This creates a fixed size vector of a predetermined length:
//Creates 5 null elements as a fixed vector;
var vec:Vector.<String> = new Vector.<String>(5, true); 

//NOTE: Can't do these methods on a fixed vector as it alters the length of it
vec.push( "Hello World" ); // ERROR!!!
vec.pop();    // ERROR!!!

vec[1] = "Hello World"; // Acceptable

So you get the idea?
If you have any questions or comments, type’em up below! :)