My JLPT practise book has these two sentences to help explain the difference between お目{め}にか
け
る
and お目{め}にか
か
る
in a context of keigo.
それでは新製品{しんせいひん}お目{め}にかけましょう。
鈴木{すずき}さんという人{ひと}に初{はじ}めてお目{め}にかかりました。
Unfortunately, the brief explanation they give about these sentences is not quite enough for me to be sure I've got it.
I think the first case, お目{め}にかける
is when you're asking someone else to look at something. "Please look at X."
And I think the second case of お目{め}にかかる
is when you're doing the looking. "I saw X."
I often get these kinds of differences mixed up. Can someone either confirm I'm right, tell me if and where I'm wrong, or enlighten me if there is some other nuance I should be aware of?