Practice variation 1 of 3
Vectors — Area formula then equal-angle circles
Your question
(i) Given that is perpendicular to with equal magnitude, show that the area of with and is .
(ii) Point lies on the circle centre radius with at angle to the horizontal. Point lies on the circle centre radius with also at angle to the horizontal. Using part (i), find that maximise the area of .
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?