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← 2020 HSC Extension 1 paper Question 11(b)

Variation 1 · answer guide

Vectors — Perpendicular parameter

Question

Find so that and are perpendicular.

This practice question was inspired by Question 11(b) in the 2020 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.Dot product: .
  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. or .

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

Verification: Substitute each back into the dot product.

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

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