Vectors — Pythagoras wording

Question

Explain the same result using a right triangle formed by , its projection , and on the line of .

This practice question was inspired by Question 14(b) 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.The shortest segment from the tip of to the line is the perpendicular, which meets at .
State the final answer clearly in the form the question requested.Any other point on the line gives a longer (or equal) hypotenuse.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Geometric form of the same orthogonality.

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