2022 HSC Mathematics Extension 1
Question 8:
Vectors
The angle between two unit vectors and is and .
Which of the following best describes the possible range of values of ?
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
- Since , .
- The inequality squares (both sides non-negative) to .
- Hence .
- For , means .
- Answer: D. (NESA multiple-choice key: D.)
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
For unit vectors, is equivalent to
Question 2
Unit vectors satisfy when
Question 3
For unit , implies