just answer to do parts $,//============================================================$

$//$ FILE: vector$3$dT$.$h

$//============================================================$

#define $\_\_$vector$3$dT$\_$H$\_\_$

#include

#include

#include

#include

#include

#include

template class vector$3$d;

typedef vector$3$d vector$3$D;

typedef vector$3$d vector$3$F;

typedef vector$3$d vector$3$I;

typedef vector$3$d vector$3$L;

typedef vector$3$D vec$3$;

template

class vector$3$d $\{//$ class that serves as both vectors and points

public:

vector$3$d$()$;

vector$3$d$($const std::string& name, int dims$)$;

vector$3$d$($const std::string& name, int dims, const std::initializer$\_$list& li$)$;

$//---------------------------------------------------------------------$

T operator$[]($int i$)$ const;

T& operator$[]($int i$)$;

$//---------------------------------------------------------------------$

std::string name$()$ const;

void name$($const std::string& name$)$;

T x$()$ const $\{$ return data$\_[0]$; $\}//$ read$-$only value of x

T y$()$ const $\{$ return data$\_[1]$; $\}$

T z$()$ const $\{$ return data$\_[2]$; $\}$

T& x$()\{$ return data$\_[0]$; $\}//$ read$-$write value of x

T& y$()\{$ return data$\_[1]$; $\}$

T& z$()\{$ return data$\_[2]$; $\}$

$//---------------------------------------$

vector$3$d& operator$+=($const vector$3$d& v$)$;

vector$3$d& operator$-=($const vector$3$d& v$)$;

$//---------------------------------------------------------------------$

vector$3$d& operator$+=($T k$)$;

vector$3$d& operator$-=($T k$)$;

vector$3$d& operator$*=($T k$)$;

vector$3$d& operator$/=($T k$)$;

$//---------------------------------------------------------------------$

vector$3$d operator$-()$;

$//---------------------------------------------------------------------$

friend vector$3$d operator$+($const vector$3$d& u$,$ const vector$3$d& v$)\{$

check$\_$equal$\_$dims$($u$,$ v$)$;

return vector$3$d$($u$.$name$\_+"+"+$ v$.$name$\_,$ u$.$dims$\_,$

$\{$ u$[0]+$ v$[0],$ u$[1]+$ v$[1],$ u$[2]+$ v$[2],0\})$;

$\}$

friend vector$3$d operator$-($const vector$3$d& u$,$ const vector$3$d& v$)\{$

check$\_$equal$\_$dims$($u$,$ v$)$;

return vector$3$d$($u$.$name$\_+"-"+$ v$.$name$\_,$ u$.$dims$\_,$

$\{$ u$[0]-$ v$[0],$ u$[1]-$ v$[1],$ u$[2]-$ v$[2],0\})$;

$\}$

$//---------------------------------------------------------------------$

friend vector$3$d operator$+($const vector$3$d& v$,$ T k$)\{$

return vector$3$d$($v$.$name$\_+"+"+$ std::to$\_$string$($k$),$ v$.$dims$\_,\{$ v$[0]+$ k$,$ v$[1]$

$+$ k$,$ v$[2]+$ k$,0\})$;

$\}$

friend vector$3$d operator$+($T k$,$ const vector$3$d& v$)\{$ return v $+$ k; $\}$

$//---------------------------------------------------------------------$

friend vector$3$d operator$-($const vector$3$d& v$,$ T k$)\{$

return vector$3$d$($v$.$name$\_+"-"+$ std::to$\_$string$($k$),$ v$.$dims$\_,\{$ v$[0]-$ k$,$ v$[1]$

$-$ k$,$ v$[2]-$ k$,0\})$;

$\}$

friend vector$3$d operator$-($T k$,$ const vector$3$d& v$)\{$ return v $*-1+$ k; $\}$

$//---------------------------------------------------------------------$

friend vector$3$d operator$*($const vector$3$d& v$,$ T k$)\{$

return vector$3$d$($v$.$name$\_+"*"+$ std::to$\_$string$($k$),$ v$.$dims$\_,\{$ v$[0]*$ k$,$ v$[1]$

$*$ k$,$ v$[2]*$ k$,0\})$;

$\}$;

friend vector$3$d operator$*($T k$,$ const vector$3$d& v$)\{$ return v $*$ k; $\}$

$//---------------------------------------------------------------------$

friend vector$3$d operator$/($const vector$3$d& v$,$ T k$)\{$

if $($k $==0)\{$ throw new std::invalid$\_$argument$("$divide by zero"$)$; $\}$

double kinv $=1\mathrm{.}0/$ k;

return v $*$ kinv;

$\}$