2022 HSC Mathematics Extension 1
Question 11(d):
Vectors
The vectors and are perpendicular.
What are the possible values of ?
How to recognise this question
Question type: vectors
- The command and notation point to vectors.
- The requested response is a worked solution.
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
- Perpendicular .
- .
- or .
- NESA: 2 marks correct; 1 mark for writing (or equivalent).
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks 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
Find so that and are perpendicular.
Question 2
Find so is perpendicular to .
Question 3
For and , find for perpendicularity.