It's a nice place to live 后面加 in 吗？ 另外 find a chair to sit 还是 find a chair to sit on? 谢谢。

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不及物动词不定式作定语时所修饰的名词如果是time,place或way,不定式后面的介词习惯上省略.但是如果是表示具体事物的名词时候，不及物动词后面介词不能省略。

time,place,way省略后面介词的例句如下：

I have no time to play (in). 

She has enough time to do look after the children (with).

The animals have to find a place to sleep (in) in winter.

This is a good place for us to study (in).

下面是方式状语的介词省略

I don't like the way he speaks (in).

I don't like the way he smiles (in).

I don't like the way he cries (in).

带介词的不定式作定语

Please give me some paper to write on.

Let"s find a room to put these things in

I have no house to live in.

He has no pen to write with.

There are five pairs to choose from.

动词不定式作定语其他用法仅供参考

(1)动词不定式与其所修饰的词之间往往有动宾关系，如果该不定式是不及物动词，或者该不定式本身有宾语，其后应有必要的介词。
He wants water to drink.

他要喝水。
She has a child to take care of.

她有一个孩子要照顾。

Are you going to the conference to be held next week?

你准备参加下周举行的会议吗？
(2)作定语的不定式可以表示情态意义。作定语的不定式有时含有情态意义，相当于may,can,will,would或should所具有的含有。
He has no friend to depend on.他没有可以依靠的朋友。（to depend on=whom he can depend on)
He is not the kind of man to do such things.他不是可能做这种事的人。（to do such things=whom may do such things)
I have a lot of work to finish today.我今天有许多工作要完成。（to finish=which I should finish或which I must finish)
(3)不定式可以修饰there be结构中做主语名词。
There is a good rule to go by.

有一项应该遵守的好制度。
There is not a moment to lose.

刻不容缓。
She knows all there is to know.

所有的事情她全都知道。
(4)不定式常用于“have+the+抽象名词”结构中。
She has the kindness to help you.

她出于好意帮助你。
I didn’t have the heart to tell you the bad news.

我不忍心把这个坏消息告诉你。
(5)有些名词后常跟不定式作定语。time,way,right,chance,reason,effort,ambition,movement。
It is already time to start spring sowing.

是开始春播的时候了。

Thank you for giving me the chance to make the speech.

谢谢你给我发言的机会。
(6)有些动词和形容词后常跟不定式，这些动词和形容词派生出来的名词后也可用不定式作定语。ability,agreement,anxiety,decision,plan,need,determination,willingness,readiness,impatience,inclination,obligation,eagerness。
例句：
His eagerness to get back home was quite obvious.

看得出他急于回家。
She made an attempt to overcome her weaknesses.

她努力克服自己的缺点。
(7)不定式可以修饰做主语的名词，相当于一个定语从句，表明动作即将发生。
The future to greet us will be bright.

我们的未来将是美好的。
The plans to be made are of vital importance.

要制定的计划至关重要。
(8)the first,the second,the last,the best,the only thing

等常跟不定式作定语。
She is always the first to answer questions.

她总是第一个回答问题。
He would be the last to agree to the plan.

他决不会同意这项计划。
(9)当go,spare作“剩下”解时，可作定语；另外还有“with/without+名词+不定式”结构。
With much money to spend,the boy was spoiled.

那个男孩花钱如流水，被惯坏了。
He left on a cold morning,without anyone to see him off.

他在一个寒冷的早上离开的，没有人为他送行。
(10)a much-to-be-longed-for place——不定式作前置定语。不定式作定语时一般需后置，但由连字符连接的不定式短语作定语则要前置，为一种简洁的表达法，其组成结构一般有“动词+名词/代词”、“动词+动词”、“动词+副词”、“形容词+动词”几类。
a do-nothing man（一个无所事事的人）
a strong-to-be-desired travel（一次十分渴望的旅行）
the take-home pay(带回家的工资）
a never-to-be-executed plan(一个永远也施行不了的计划）