In mathematics, what is a quantity having both direction and magnitude?

In July 1941, who was made a lieutenant general and named commander of U.S. Army forces in the Far East? In Latin America, which largest New World cat is commonly called "el tigre"? Which actress sang "Aloha ʻOe" in "Lilo & Stitch", where she voiced Nani? In March 2001, President George W. Bush decided not to regulate emissions of which gas from power plants? In Mississippi there's a town called Coldwater, as well as a Hot... what beverage? In Moscow's Teatralnaya Square, you can see a show at which famous opera and ballet theater? In November 1971, which man hijacked a plane and parachuted out with $200,000, never to be seen again? In October 1973, which late-night NBC talk show debuted with Tom Snyder as host?