TestMum
← 2022 HSC Extension 1 paper Question 14(b)

Variation 2 · answer guide

Vectors — Expand algebraically

Question

For fixed , let . Show is minimised at .

This practice question was inspired by Question 14(b) in the 2022 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

  1. Set up the solution: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required..
  2. Finish the calculation, then check that the result meets the question’s conditions..
  3. State the final answer clearly in the form the question requested. so minimum.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Calculus proof of the projection formula.

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

← Back to 2022 HSC Extension 1 paper Question 14(b)