I'm always troubled when I read prose which abuses the lowly preposition.
"I turned my head up and looked at her."
"I ended up looking at my feet."
"He stared the other man down."
Prepositions (most of them) require the presence of an object (noun or pronoun) to make a complete prepositional phrase in standard usage. As a phrase, they may function as nouns, adjectives, or adverbs--the preposition itself denotes temporal, spatial, or logical relationship (e.g., it shows where the object "is" in space or time).
In sentence one, there is no object. A reader asks herself, "Up where?"
A suggested revision: "I turned and looked at her." Less words (usually) = better sentence.
In sentence two... Well, let's just say it doesn't work.
A suggested revision: "In the end, I looked at my feet." Or "I eventually looked at my feet."
While we use the phrase "stare down" in common language, it bothers me. I still want to ask myself, "Down where?"
A suggested revision: "He stared at the other man." Or "He stared until the other man flinched."
Please take care of your prepositions. They're like delicate flowers.