Variation 3 · answer guide
Vectors — Cubic from perpendicularity
Question
Show that if , then , and solve this cubic.
This practice question was inspired by Question 12(a) in the 2024 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Step by step
- Set up the solution: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required.Dot product expands to .
- Finish the calculation, then check that the result meets the question’s conditions.Factor as .
- State the final answer clearly in the form the question requested.Answer: .
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: Synthetic division by yields .
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2024 HSC Extension 1 paper Question 12(a)