I had a real challenge trying to convince my year 11s today of the awe-and-wonder of vectors and how we could have achieved little as a human race without them. I explained how I used to design buildings taking advantage of the wonderful addition properties of vectors by taking all the forces on a building and summing them such that I could design the building just to resist their single resultant force. They didn’t see the beauty of it so here’s my second ploy:
We’ve all seen the ‘canoeist crosses a river’ vector question where the the flow of water in the river ensures they take a diagonal path rather than one perpendicular to the bank. The following approach is an alternative take on this kind of problem.
First start by showing them this video:
Next, ask them how they think vectors might be involved in getting those planes to land safely.
After that, set them this problem:
Scroll through the slides to view the solution.
If ever you want a real world example of how vital vectors are then this should hopefully convince your students!