TestMum
← 2020 HSC Extension 1 paper Question 6

Variation 2 · answer guide

Vectors — Geometric meaning

Question

Vectors and start at the same point and end at and . Which statement describes ?

  1. The directed segment from to
  2. The directed segment from to
  3. The directed segment from to the midpoint of
  4. The directed segment from to

This practice question was inspired by Question 6 in the 2020 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.So runs from to .
  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: Position-vector identity: .

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

← Back to 2020 HSC Extension 1 paper Question 6