Using "that...in" instead of "in which"

Is it grammatically correct to say the following?

What we are doing is not being interpreted in the way that it was meant in.

Instead of...

what we are doing is not being interpreted in the way in which it was meant.

I would appreciate it if you could specify the academic basis if possible.

Solution 1:

When using a that relative with the the head noun way, the preposition in is usually not included and the relativized element is an adjunct of means (how), not the object of a preposition.

This process of learning is hardly an explicit one, it is the way that tacit knowledge is acquired -- learned. (Studies in the Education of Adults; Learning expertise in practice: Implications for learning theory; JARVIS, PETER)

not

?This process of learning is hardly an explicit one, it is the way that tacit knowledge is acquired in -- learned in.

So the gap for the understood element is simply the whole adjunct.

tacit knowledge is acquired (how?)

Further examples in academic literature:

One of the most notable benefits of the digital revolution is the way that it facilitates collaboration. (Chronicle of Higher Education; The Job-Market Moment of Digital Humanities)

The potential for such moderation to emerge is visible in the way that Sunni tribal leaders in Iraq have turned against al Qaeda to work with us; they could not stand the thought of living under such fundamentalism and brutality. (Foreign Affairs; America's Priorities in the War on Terror; Huckabee, Michael D.)

It did not repeal the Militia Clauses in the way that the Twenty-First Amendment repealed the Eighteenth. (Michigan Law Review; THE SECOND AMENDMENT: STRUCTURE, HISTORY, AND CONSTITUTIONAL CHANGE; Yassky, David)

In fact, I've not come across an example with in, and so suspect that it is excluded.

Examples on the Web:

When 'gastronomy' was on the margins of attention it seemed big because it was an unexpected way to get at everything -- the nature of hunger; the meaning of appetite; the patterns and traces of desire; tradition, in the way that recipes are passed mother to son; and history, in the way that spices mix and, in mixing, mix peoples. (The Atlantic)

The parallels lie thick on the ground here, though, as I noted earlier, not quite precisely in the way that Murray saw them. (Marquette)

While the economic downturn must have some impact on legal immigrants, there is no indication that their numbers have fallen in the way that that those for illegal immigrants have declined. (Center for Immigration Studies)

Sceptics have sometimes questioned the effectiveness of international law, as it can not be enforced in the way that police forces preserve national laws. (UN)