The manager was unaware of the points engaged, so his understanding about the matter was quite arbitrary.(过去分词作后置定语）

=The manager was unaware of the points which were engaged, so his understanding about the matter was quite arbitrary.（定语从句作后置定语）

句中engaged意思为“参与，从事，涉及到，所谈及到，”

He is engaged in a game of tennis.
他现在从事于打网球。

He engages in a game of tennis every morning．
他每天早晨忙于打网球。

The professor is engaged in advanced studies.
该教授正进行高深的学术研究。

I couldn't get him as the line was engaged.
因电话占线，我没能挂通他的电话。

Jack and Anne are engaged.
杰克和安妮订婚了。

There were six engaged couples at the party.
宴会席上有六对订婚夫妇。

They found the three engaged in target practice.  

他们发现那3个人在练习打靶。

the various projects he was engaged on.  

他参与的各种项目

A:engage  具体意思如下

(1)vi.参与;从事 

I have never engaged in the drug trade. 

我从未参与过毒品交易。

 You can engage in croquet on the south lawn.  

你可以参加南边草坪上的槌球游戏。

(2)vt.吸引（人）;引起（注意、兴趣）

They never learned skills to engage the attention of the others.  

他们从未学过吸引他人注意的技巧。

(3)vt.使参与，使参加（谈话） 

They tried to engage him in conversation.

他们试图跟他交谈。

 We want to engage recognized leaders in discussion.  

我们想和公认的领袖们进行讨论。

(4)vi.适应；（与…）建立密切关系 

She found it hard to engage with office life.  

她发现很难适应办公室生活。

 She had vowed to go out of her way to engage with the Irish people at local community level.  

她已经发誓要努力和当地的爱尔兰人建立关系。

(5)vt.任命;聘用;雇用

 We engaged the services of a recognised engineer.  

我们雇用了一个公认的杰出工程师。

 He had been able to engage some staff.  

他已经能够雇用一些员工。

(6)vi.（使）啮合;（使）咬合 

Press the lever until you hear the catch engage.  

压下挡杆，直到听到挡挂好。

a lesson in how to engage the four-wheel drive.  

如何使四轮驱动啮合的课程

(7)vt.与…交战 

It could engage the enemy beyond the range of hostile torpedoes.  

从这可以避开敌方鱼雷区对敌人发动进攻。

B:arbitrary  adj.武断的;任意的;任性的;主观的 

Arbitrary arrests and detention without trial were common.  

随意逮捕和拘留屡见不鲜。

C:be unaware of 不知道, 没有察觉到, 没有意识到

I was unaware of his existence until now.
现在我才知道有他这么个人。

He was unaware of his mistakes.
他没有意识到自己的错误。

You seem be unaware of how urgent the situation is.  

你好像没有意识到形势是多么的急迫.

To be unaware of imminent danger or trouble.  

因为可能的危险或者麻烦而令人不适.

You can totally be unaware of this score.  

这个分数,你完全可以不在乎.

You can hardly be unaware of the manner in which I suffered at his hands.  

你难道不知道他是如何对我的吗?