2024 HSC Mathematics Extension 1
Question 11(a):
Vectors
Consider the vectors and .
(i) Find .
(ii) Find .
How to recognise this question
Question type: vectors
- The command and notation point to vectors.
- The word “hence” means the later part is intended to reuse the earlier result.
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
- (i) . Then .
- NESA 11(a)(i): 1 mark for the correct answer (or equivalent ).
- (ii) .
- NESA 11(a)(ii): 1 mark for the correct scalar .
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
Let and .
(i) Find .
(ii) Find .
Question 2
Let and .
(i) Find .
(ii) Find .
Question 3
Let and .
(i) Find .
(ii) Find .