Variation 1 · answer guide

Vectors — Scale only the projected vector

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.Projection is linear in its first argument: .
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: Formula: numerator gains a factor ; denominator unchanged.

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