[racket] please help to change vector to list

Hi ALL,

I have this code

(define test
  (lambda (x v)
    (define helper
      (lambda (ls)
        (cond
          ((empty? ls) '())
          ((empty? (rest ls)) '())
          ((equal? (second ls) x) (cons (first ls) (helper (rest
ls))))
          (else (helper (rest ls))))))
   (helper (vector->list v))))

When I run it with
> (test 'a #(b a c a))
it returns
'(b c)

Is there a way to use the list such as (test 'a '(b a c a))?  I tried to
delete vector->list from the last line of the code, but it did not work.
Why?

Thanks a lot
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