Practice variation 1 of 3
Vectors — Dot identity and parallelogram case
Your question
(i) For a vector , show that .
(ii) In the trapezium , is parallel to and . Let , and , where . Using part (i), or otherwise, show that . Hence deduce that if , then .
This practice question was inspired by Question 14(c) in the 2021 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?