2020 HSC Mathematics Extension 1
Question 11(b):
Vectors
For what value(s) of are the vectors and perpendicular?
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
- Two non-zero vectors are perpendicular iff their dot product is zero.
- Compute .
- Solve .
- Hence or .
- NESA: 3 marks correct; 2 marks for evaluating the dot product and setting it to 0; 1 mark for writing a dot product .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 3 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 that is perpendicular to .
Question 3
Find so that is perpendicular to .