finding line in plane perpendicular to another line

Question

I have a vector that I need to find. It is in the (111) plane. The vector I need to find is perpendicular to another vector which is parallel to [01-1].

To be clear:

I want to find A which lies in the (111) plane. Another vector, B, is parallel to [01-1] A is perpendicular to B.

How can I find A?

Would I take the cross product of (111) and [01-1]?

Answer 1

Yes you need a vector which is perpendicular to the normal $(1, 1, 1)$ of the plane and perpendicular to $(0, 1, -1)$, so you need to work out the cross product