This is a worksheet which introduces some of the ideas contained within the 3-d geometry section of A-level maths: vector equations of lines and planes and testing whether or not points lie on these planes. The latter questions also give students an idea of linear dependence, although this understanding isn’t strictly necessary for the A-level course.
It’s in the context of getting from one planet (coordinate) to another using the buttons (direction vectors) in a spacecraft.
I’ve used this as an initial introduction to vectors, as was the norm at my previous school (from where I stole the idea – I think it comes almost directly from Robert Wilne). More recently I’ve used it as an introduction to 3-d vectors, after previously teaching 2-d vectors and this has been more effective as the pupils have a better toolkit of terminology to help them solve the problems, but the context seems to make the leap from lines to planes more intuitive.
And it’s called hyperspace hopping, so it’s fun! Enjoy.