2025 HSC Mathematics Extension 1
Question 8:
Vectors
Points and have non-zero, non-parallel position vectors and . Point has position vector . The points , and lie on the same line. Which statement must be true?
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
- gives .
- Thus the vector from A to C points in the same direction as the vector from B to A.
- The order is B–A–C, so A lies between B and C: option A.
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
Find the projection of onto .
Question 2
Find if is parallel to .
Question 3
Find the angle between and .