Generic term for 'row' and 'column'

I think the word he is look for is "vector"; i.e. a line of indeterminate length in a specific direction.

How about axis?

1. (Mathematics) one of two or three reference lines used in coordinate geometry to locate a point in a plane or in space.

(Collins English Dictionary – Complete and Unabridged)

Update:

You say you're looking for a name for a code variable. Seeing as people here struggle so much to find such a word, I'm guessing whatever you settle on will confuse whoever reads your code just as much. I'd just skip trying to be pithy and go for rowOrColumn. Clarity over brevity.

Thank you all for your suggestions. I need this term for a logical function name in an assignment for students who aren't programmers, so a lot of the words put forward here would not mean much to them.

I asked a colleague about it and he suggested 'line'. I'll use this as it makes logical sense for the match 3 game example project they will be completing, and I thought I'd return and share.