replacement of "how" with "the way"

Question

wordreference.com:
(1) He had a clear vision of how he hoped the company would develop. — correct
(2) He had a clear vision how he hoped the company would develop. — correct

As far as I know, if a sentence is not interrogative and not exclamative — i.e. when "how" doesn't stand at the beginning of a sentence and when a how-clause is a part of a complex sentence — we can always replace "how" with "the way". So I did it in (1) & (2):
(3) He had a clear vision of the way he hoped the company would develop.
(4) He had a clear vision the way he hoped the company would develop.
(5) He had a clear vision in the way he hoped the company would develop.

Could you tell me please which of them are correct and which are not?

Answer 1

As a native speaker, who never learned English by rule, I think number 3 is perfect. Numbers 4 and 5, are neither grammatical nor idiomatic, in my view.

The word vision does require a preposition of some kind - "of" is clearly correct, another might be "about". One could say:

"He had a clear vision about the way he hoped the company would develop."

I do not consider number 2 of your examples with how to be correct. You need an "of" or an "about" in front of "how".

In these sentences you could also substitute a suitable "---ing" verb for the preposition e.g

"He had a clear vision involving the way/how he hoped the company would develop". Other possibilities might be: depicting/detailing/regarding. Or you could say "He had a clear vision as regards the way/how the company would develop."