Practice variation 2 of 3
Vectors — Area formula then double-angle circles
Your question
(i) Using a perpendicular vector of equal magnitude, show that the area of is .
(ii) Hence, with and , show the area of is (up to an equivalent non-negative form), and find maximising the area.
This practice question was inspired by Question 14(c) 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.
Before you check
- Have you stated every choice or assumption?
- Can another student follow each line?
- Did you verify the final result independently?