TestMum
← 2021 HSC Extension 1 paper Question 5

Variation 1 · answer guide

Vectors — Positive dot product

Question

If for nonzero vectors , which statement MUST be true?

  1. The angle between and is acute
  2. The angle between and is obtuse
  3. The angle is a right angle
  4. is negative

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. for nonzero magnitudes, so is acute.
  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: Example: and the angle is .

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

← Back to 2021 HSC Extension 1 paper Question 5