Variation 3 · answer guide

Vectors — Both scaled differently

Question

If , the projection of onto is

This practice question was inspired by Question 6 in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required.Scaling by multiplies the projection by ; scaling by has no effect.
Finish the calculation, then check that the result meets the question’s conditions.Result .
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: Same reasoning as the 2023 paper with factors and .

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