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← 2021 HSC Extension 1 paper Question 5

Variation 2 · answer guide

Vectors — Zero dot product

Question

If and are nonzero, which MUST be true?

  1. The vectors are perpendicular
  2. The vectors are parallel
  3. The angle is obtuse
  4. One vector must be the zero vector

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. (in ).
  2. 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: and the vectors are orthogonal.

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

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