Examples:

• It will be difficult for us to be successful if we continue working at cross-purposes.
• Yesterday, we were at cross-purposes with Steve. We had a conversation about Georgia, only to realize later that I was talking about Georgia in Russia but he was talking about Georgia in the U.S.
• Sam and I were at cross purposes the other day. We had a talk about Kevin, but I was talking about Kevin my brother, but he thought we were talking about our mutual friend also called Kevin.
• Today I was discussing football matters with an Asian friend, but we were at cross-purposes. All the while, I was discussing American football, but he thought I was talking about soccer.
• The members of Lord’s House fear the two government departments are working at cross purposes.