POWER OF ATTORNEY

        The undersigned constitutes and appoints Joel Rubinstein, Rupa Briggs,
Daniel Nussen, Anastasiya Lisovskaya, Jordan Leon and Elizabeth Mapelli, or any
of them acting singly, as the undersigned's true and lawful attorneys-in-fact
and agents, with full power of substitution and resubstitution, for the
undersigned and in the undersigned's name, place and stead, to:

        1.   prepare, sign, and submit to the Securities and Exchange Commission
(the "SEC") on its Electronic Data Gathering, Analysis, and Retrieval ("EDGAR")
Filer Management website a Form ID application, including any amendments and
exhibits thereto, and any other related documents as may be necessary or
appropriate, to obtain from the SEC access codes to permit filing on the SEC's
EDGAR system, granting unto said attorneys-in-fact and agents, and each of them,
full power and authority to do and perform each act and thing requisite and
necessary to be done as required by any rule or regulation of the SEC and the
EDGAR Filer Manual as fully and to all intents and purposes as the undersigned
might or could do in person, hereby ratifying and confirming all that said
attorneys-in-fact and agents, and each of them, may lawfully do or cause to be
done by virtue hereof; and

        2.   sign any and all SEC statements of beneficial ownership of
securities of Zanite Acquisition Corp. (the "Company") on Schedule 13D as
required under Section 13 and Forms 3, 4 and 5 as required under Section 16(a)
of the Securities Exchange Act of 1934, as amended, and any amendments thereto,
and to file the same with all exhibits thereto, and other documents in
connection therewith, with the SEC, the Company and any stock exchange on which
any of the Company's securities are listed, granting unto said attorneys-in-fact
and agents, and each of them, full power and authority to do and perform each
act and thing requisite and necessary to be done under said Section 13 and
Section 16(a), as fully and to all intents and purposes as the undersigned might
or could do in person, hereby ratifying and confirming all that said attorneys-
in-fact and agents, and each of them, may lawfully do or cause to be done by
virtue hereof.

        A copy of this power of attorney shall be filed with the SEC.  The
authorization set forth above shall continue in full force and effect until the
undersigned revokes such authorization by written instructions to the attorneys-
in-fact.

        The authority granted hereby shall in no event be deemed to impose or
create any duty on behalf of the attorneys-in-fact with respect to the
undersigned's obligations to file a Form ID, Schedule 13Ds and Forms 3, 4 and 5
with the SEC.


Dated: September 23, 2020


                                        By: /s/ John Veihmeyer
                                            ------------------
                                            Name:  John Veihmeyer