Vectors — Perpendicular vectors find parameter

Question

The vectors and are perpendicular. Find all possible values of .

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.

Set up the solution: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required.Dot product: .
Finish the calculation, then check that the result meets the question’s conditions.Factor .
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: Check : .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.