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← 2024 HSC Extension 1 paper Question 13(c)

Variation 3 · answer guide

Vectors — Different basis vectors

Question

Let and . If and , find in terms of and .

This practice question was inspired by Question 13(c) 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

  1. Set up the solution: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required. and .
  2. Finish the calculation, then check that the result meets the question’s conditions.Add: ; subtract: .
  3. 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: Orthogonal basis makes the system diagonal after sum/difference.

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

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