请教一题关于定语从句的英语题

1.此题并非定语从句,而是“疑问词 + 不定式”短语作后置定语的用法.
2.“疑问词 + 不定式”短语是英语中比较常见的一种语法现象,它相当于一个名词短语,但有时候亦可作后置定语.
1）I don't know what to do.
what to do做know的宾语.
2）The problem is how to do it.
how to do it做is的表语.
3.此题on which to base his(their?) choices about their eating habits是belief的后置定语.
其中：on which to base his choices about their eating habits = which to base his choices on about their eating habits
= to base his choices about their eating habits on which
而which to base his choices on about their eating habits正是“疑问词 + 不定式”结构,它做belief的后置定语,而about their eating habits又是choices的后置定语.
4.既然是“疑问词 + 不定式”结构,不定式中当然含有符合to.
句子翻译：有时候,人们没有一定的,可以做为他们关于饮食习惯方面的选择基础的信条.