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← 2022 HSC Extension 1 paper Question 6

Variation 2 · answer guide

Vectors — Wrong diagonal

Question

The vector cannot be the projection of onto

  2. (same line, but check orientation/length separately)
  4. a positive multiple of

This practice question was inspired by Question 6 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. is parallel to and to , not to .
  2. Match the result to the choices and state the correct option.Therefore option C is correct.

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

Verification: Opposite diagonals are orthogonal, not parallel.

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

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