‘What will you do / are you doing tomorrow evening?’ ‘Nothing. I’m free.’
(Essential Grammar in Use)
The book says ‘are you doing’ is correct. But I don’t know why ‘will you do’ is not correct?
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As snailboat pointed out in a comment on your question, the premise of this question is mistaken. "What will you do tomorrow?" is grammatical, acceptable and idiomatic in certain circumstances. For example:
Anna: Oh no! My running shoes are ruined! Now I won't be able to go for my usual evening run tomorrow.
Joel: Oh dear! What will you do tomorrow evening instead?
The difference between "What will you do tomorrow?" and "What are you doing tomorrow?" is not a question of grammaticality - both are grammatical - or even one of how idiomatic the sentence appears. The difference is what the question is asking:
"What are you doing tomorrow?" is a question that asks the listener what plans they have already made for tomorrow. It is passive, and is merely asking for information from the listener.
"What will you do tomorrow?" is a question that asks the listener to make a decision about what to do tomorrow. This question is more active. It asks the listener to create a plan and then tell the questioner what the newly formulated plan is.
Consequently, after some event that forces the listener to change their plans for tomorrow, "What will you do tomorrow [now that your previous plan is no longer valid]?" is more idiomatic than "What are you doing tomorrow [now that your previous plan is no longer valid]?", because there has not been time to produce a new plan, and the listener must therefore create a new one, rather than merely recite the plan that they had already made.
In contrast, if the listener has indicated that they are busy tomorrow, "What are you doing tomorrow?" is more appropriate, since the implication is that the listener has already made plans, and the questioner is inquiring what those plans might be.
There is also a small difference in subtext to the two questions as well. "What are you doing tomorrow?" is more passive, but also includes a possible subtext of asking whether the questioner can join in the activity. "What will you do tomorrow?" on the other hand contains a possible subtext of asking what the listener will do without the speaker, and can thus be construed as more cold.
Well, I don't know the exact reason why the sentence "will you do" is incorrect but I can put some light related to this.
Please have a look at below link and read first three pages:-
As there is no future tense, it could be a reason for "will you do" is not correct.