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← 2022 HSC Extension 1 paper Question 13(a)

Variation 2 · answer guide

Vectors — Rhombus diagonals

Question

Explain why and are perpendicular when .

This practice question was inspired by Question 13(a) 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.They are diagonals of a rhombus formed by and .
  2. State the final answer clearly in the form the question requested.Diagonals of a rhombus are perpendicular; equivalently expand the dot product.

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

Verification: Geometric reading of the same algebra.

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

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