There are very few lexical words (that is, not counting interjections) without vowel letters. The longest such lexical word is tsktsks, pronounced /tsktsks/. The mathematical expression nth /n/, as in delighted to the nth degree, is in fairly common usage. Another mathematical term without vowel letters is rng /r/, derived from ring by deleting the letter i. A more obscure example is ln.

is there a word in the english language that does not have a vowel?

OPT:
a). no;
b). yes;
b).