Objective: This assignment will help you review the ArrayList class as a type$-$safe generic data type.

Program assignment: Build an ADT for vectors.

Your program should have the following header:

A vector $x$ consists of $n$ real components $x_1,x_2,$dots,$x_n.$ The operations between two vectors $,$

$\{$:$x_n]$ and $y=[y_1,y_2,$dots,$y_n]$ are defined as follows:

addition

$x_1+y_1,x_2+y_2,$dots,$x_n+y_n$

subtraction

$x_1-y_1,x_2-y_2,$dots,$x_n-y_n$

dot$-$product

$x*y=x_1**y_1+x_2**y_2+$dots$+x_n**y_n$

equivalence

$x==yif(x_1=y_1$ and $x_2=y_2$ and dots and $x_n=y_n)$

scalar$-$product

$s**x=[s**x_1,s**x_2,$dots,$s**x_n],$ where $s$ is a real number.

absolute$-$value

$|x|=\sqrt[\phantom{2}]{?}(x*x)$

You should have two constructors:

a$.$ One constructor, with parameters $($double $[]$ initvalues$),$ where initvalues are

the initialization values for the new vector.

b$.$ The copy constructor.

You should have an accessor function for the $k-$th components of a vector.

You should have member functions for arithmetic: plus $()$ and minus $()$ which, for example, would

be used as: $x=y.$plus$(z),$ where $x,y,$ and $z$ are MyVector objects.

You should have a member function for scaling: scaledBy $()$ which, for example, would be used as:

$x=y*scaledBy(s),$ where $x$ and $y$ are MyVector objects, and $s$ is a real number.

You should override the toString $()$ method for display on System. out

You should override the equals $()$ method.

You should create an absolute value function: abs $()$

You should build a dot product function: dot $()$ Design specifications

Create a Java project project $8$ and a package package $8$

Call your class MyVector. Define a second class containing a main method that exercises the class

MyVector as an application. That is$,$ a main method that runs through a selection of arithmetic and

logical operations and uses MyVector output. The two classes should be saved in two different files.

Your class MyVector should keep the vector in an ArrayList