2021 HSC Mathematics Extension 1
Question 1:
Vectors
Given that and , what is ?
How to recognise this question
Question type: vectors
- The command and notation point to vectors.
- The requested response is a multiple choice.
How to handle it: write the vector relationship component by component, then use a dot product, magnitude or scalar multiple as required.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- By definition .
- .
- Option A mixes components; B reverses the subtraction with mixed signs; D is .
- Answer: C. (NESA multiple-choice key: C.)
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Given and , what is ?
Question 2
If and , what is ?
Question 3
Given and , find .