I do love a little challenge for A-level Further Maths students. They are often confident and very capable mathematicians, but occasionally overlook the small details. This challenge looks into which strategies students use when working with 3D vectors, lines and angles.
The most annoying thing? There is no single correct answer.
What is the investigation?
Students start with two points, create a line, construct two perpendicular lines and then join up the lines – did they create a square? How do you know? Justify it?
Cool vectors can be exciting! They can describe the motion of a particle, they can represent the acceleration of a rocket, they can tell you about the angle an impact takes place at!
Uncool vectors describe lines, they can intersect, they could be perpendicular, they could even describe skew lines in three-dimensions. Not quite as exciting. It isn’t difficult to see that revising standard C4 vectors can be a tad dull. How about an investigation? An investigation without an obvious answer. A question so simple that the answer is a single number. It’s the steps in between that make things interesting…
I asked my A-Level class to find the area of a rectangle … simple so far, how is this worthy of C4?
The rectangle is bounded by four vector equations … ok, points of intersection, line segment length, bit of Pythagoras there
The vector equations are 3D … ooh, that makes it a bit harder
There are eight equations to choose from … that’s mean, that means finding the angle between lines, checking for skewness, identifying parallel vectors
There are plenty of ‘red herrings’ … now that is just unfair (great!)
The solution to the problem is a simple surd. If you do ‘Crack the Code’ or ‘Locked Box’ problems you could use the digits under the square root sign as your padlock code.