Learn Hardcore Dutch: Die collectie bevat een kunstwerk waarvan het ontwerp door Tom is getekend. - That collection contains an artwork whose design was drawn by Tom.

Die is a demonstrative pronoun meaning “that” (or “this”) referring back to collectie. In Dutch, all de-words (common gender nouns) take die for both singular and plural (“die man”, “die boeken”), whereas dat is only used for singular het-words (“dat huis”, “dat kind”). Since collectie is a de-word, you must use die.

What is the function of waarvan in “een kunstwerk waarvan het ontwerp … is getekend”?

Waarvan is a relative pronoun meaning “of which” or “whose”. It links the main clause (een kunstwerk) to the subordinate clause (het ontwerp door Tom is getekend) and indicates possession or association. In English you’d say “an artwork whose design was drawn by Tom”.

Why is the clause “het ontwerp door Tom is getekend” in the passive voice, and how is that formed in Dutch?

It’s passive to focus on het ontwerp (the design) as the subject, not Tom. Dutch forms the passive with the auxiliary zijn (“is”, “was”) plus a past participle. Here:
• Subject: het ontwerp
• Auxiliary: is
• Past participle: getekend
So het ontwerp is getekend literally means “the design has been drawn” (or “was drawn”).

Why is the agent Tom introduced by door, and could you use van instead?

In Dutch passive constructions, the doer is always introduced with door (just like English “by”). You cannot use van for the agent in a true passive. Van is reserved for possession or origin, not for marking the actor of a passive verb.

Why is the auxiliary verb is used here instead of heeft (“has”) as in an active perfect?

In an active perfect you’d say Tom heeft het ontwerp getekend (“Tom has drawn the design”). In a passive, however, Dutch uses zijn (is, was) + past participle. So you switch the auxiliary from hebben (“to have”) to zijn (“to be”) to form the passive perfect: is getekend.

Could you rewrite this sentence in an active voice? If so, how?

Yes. For example:
Tom heeft het ontwerp van dat kunstwerk getekend.
Here
• Tom is subject,
• heeft getekend is the active perfect,
• het ontwerp van dat kunstwerk specifies which design.

What’s the difference between ontwerp and tekening in Dutch?

Ontwerp means design (the conceptual plan or blueprint), while tekening is a drawing (the actual sketch or picture). The verb tekenen means “to draw,” but the noun ontwerp refers to the plan that someone drew, not the physical drawing itself.

Is waarvan the only option to express “of which,” or could you use welke or a split form?

For “of which,” waarvan is the standard relative pronoun. You cannot use welke by itself to mean “of which.” Colloquially you might hear a split construction like een kunstwerk waar het ontwerp ervan door Tom is getekend, but that’s wordy. Waarvan is concise and correct.

Why is there no comma before waarvan in the sentence?

In Dutch, restrictive relative clauses (those that define exactly which item you mean) are not set off by commas. Since een kunstwerk waarvan … tells you which artwork, it’s restrictive and therefore unpunctuated.

Could you say een ontwerp instead of het ontwerp in this sentence?

You could grammatically, but it changes the meaning. Een ontwerp means “a design” (unspecified), whereas het ontwerp refers to the specific design of that artwork. The original wants to point to that particular design. Using een ontwerp would leave it vague.