** Using WeBWorK **

One way to remove the variables from the context is

    Context()->variables->remove('x','y','z');

Another would be

    Context()->variables->clear();

But if you are adding new variables, the easier is to use are() rather than add(), which first removes all the existing variables and adds the new ones. So replace

    Context()->variables->remove(x); # only variables should be n 
    Context()->variables->add(n=> 'Real');  
    # how to remove y and z from Vector context?

with

    Context()->variables->are(n => 'Real');

There are several other things you probably want to change as well. First, you probably want to disable a coupe of reduction rules that reorder or regroup the terms of your expressions. You can use

    Context()->noreduce("(-x)+y","(-x)-y");

to do that. This should keep your terms in the same order you gave them originally.

Next, it looks like you have used a pretty old problem as a starting point, so have some old-style code that should be updated.

Change

    TEXT(&beginproblem);

to

    TEXT(beginproblem());

Change

    TEXT(EV2(<<EOT));
    ...
    EOT

to

   BEGIN_TEXT
   ...
   END_TEXT

and

    SOLUTION(EV3(<<'END_SOLUTION'));

to

   BEGIN_SOLUTION

and that will being you more up to date.

Davide