HELP PLEASE on finding angles in three dimensional figures with the help of unit...

[lightspeed]

...vectors? There's an item in my homework that I can't figure out. I think I've already spent two hours on it. Actually, this is my first time to meet such topic. Here's the question: In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the carbon atom at the center. In coordinates where one of the C---H bonds is in the direction of i+j+k (these letters have caret or "hat" above them because they are unit vectors), an adjacent C---H bond is in the i-j-k (unit vectors too) direction. Calculate the angle between these two bonds.

I know from Chemistry that it's 109.5 degrees. But this subject is Physics and we need to show how we get our answer. I'm asking if you can at least teach me how to get angles using those conditions (especially if it has something to do with unit vectors). I really don't have a clue. I don't want to cheat. I just want to learn. Thank you very much!!! God bless!!!