Write a class called Vec$2$D$.$ The required methods are shown in the code snippet below. The comment indicates the action of the method and what is returned.

A quick review of the dot product:

Take two vectors, each with Cartesian components x and y: $$a $=($ax$,$ ay$)$ and $$b $=($bx$,$ by$).$ The dot product of vectors $$a and $$b results in a scalar and is given by:

$$a $$b $=$ axbx $+$ ayby

class Vec$2$D$()$:

def $\_\_$init$\_\_($self$,$ x$,$ y$)$:

$"""$Store x and y in a form of your choosing."""

def $\_\_$str$\_\_($self$)$:

$"""$Returns string of form $\text{'}($x$,$ y$)\text{'}"""$

def $\_\_$repr$\_\_($self$)$:

$"""$Returns string of form 'Vec$2$D$($x$,$ y$)\text{'}"""$

def get$\_$x$($self$)$:

$"""$Getter for x$.$ Returns x$."""$

def get$\_$y$($self$)$:

$"""$Getter for y$.$ Returns y$."""$

def set$\_$x$($self$,$ x$)$:

$"""$Setter for x$."""$

def set$\_$y$($self$,$ y$)$:

$"""$Setter for y$."""$

def $\_\_$add$\_\_($self$,$ b$)$:

$"""$Vector addition of self and b$.$ Returns a Vec$2$D object."""

def $\_\_$sub$\_\_($self$,$ b$)$:

$"""$Vector subtraction: self $-$ b$.$ Returns a Vec$2$D object."""

def $\_\_$mul$\_\_($self$,$ scalar$)$:

$"""$Multiplication on left of Vec$2$D and scalar: self $*$ scalar. Returns Vec$2$D

$,->$ object."""

def $\_\_$rmul$\_\_($self$,$ scalar$)$:

$"""$Multiplication on right of Vec$2$D and scalar: scalar $*$ self. Returns Vec$2$D

$,->$ object."""

def length$($self$)$:

$"""$Computes length of the vector. Returns a float."""

def dot$($self$,$ b$)$:

$"""$Computes dot product of self and b$.$ Returns a float."""

Sample:

$>>>$ a $=$ Vec$2$D$(3\mathrm{.}0,0\mathrm{.}0)$

$>>>$ a

Vec$2$D$(3\mathrm{.}0,0\mathrm{.}0)$

$>>>$ print$($a$)$

$(3\mathrm{.}0,0\mathrm{.}0)$

$>>>$ a$.$get$\_$x$()$

$3\mathrm{.}0$

$>>>$ a$.$get$\_$y$()$

$0\mathrm{.}0$

$>>>$ b $=$ Vec$2$D$(0\mathrm{.}0,0\mathrm{.}0)$

$>>>$ b

Vec$2$D$(0\mathrm{.}0,0\mathrm{.}0)$

$>>>$ b$.$set$\_$x$(0\mathrm{.}0)$; b$.$set$\_$y$(4\mathrm{.}0)$

$>>>$ b

Vec$2$D$(0\mathrm{.}0,4\mathrm{.}0)$

$>>>$ c $=$ a $+$ b

$>>>$ c

Vec$2$D$(3\mathrm{.}0,4\mathrm{.}0)$

$>>>$ d $=$ a $-$ b

$>>>$ d

Vec$2$D$(3\mathrm{.}0,-4\mathrm{.}0)$

$>>>$ a$*3$

Vec$2$D$(9\mathrm{.}0,0\mathrm{.}0)$

$>>>4\mathrm{.}5*$b

Vec$2$D$(0\mathrm{.}0,18\mathrm{.}0)$

$>>>$ c$.$length$()$

$5\mathrm{.}0$

$>>>$ d$.$length$()$

$5\mathrm{.}0$

$>>>$ a$.$dot$($b$)$

$0\mathrm{.}0$