Variation 2 · answer guide

Vectors — Scale only the direction

Question

If , then equals

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.Any nonzero multiple of spans the same line, so the projection is unchanged.
Finish the calculation, then check that the result meets the question’s conditions.In the formula, factors of cancel between numerator and denominator.
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: Projection depends on the line, not the particular direction vector length.

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