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← 2021 HSC Extension 1 paper Question 5

Variation 3 · answer guide

Vectors — Component reading of sign

Question

For and , which is true?

  1. so the angle is obtuse
  2. so the angle is acute
  3. so the angle is right
  4. The angle cannot be determined from the components

This practice question was inspired by Question 5 in the 2021 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.Negative dot product obtuse angle.
  3. Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: Magnitudes positive, so sign of matches the sign of the dot product.

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

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