Variation 2 · answer guide

Vectors — Sum longer than $\sqrt{2}$

Question

Unit vectors satisfy when

This practice question was inspired by Question 8 in the 2022 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..
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: Square both sides and solve for .

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