2020 HSC Mathematics Extension 1
Question 4:
Vectors
Maria starts at the origin and walks along all of the vector , then walks along all of the vector and finally along all of the vector .
How far from the origin is she?
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
- Add the three displacements componentwise: .
- Distance from the origin is the magnitude of the resultant: .
- Option C adds two path lengths rather than using the resultant; option D adds three separate magnitudes; option A comes from a wrong component sum.
- Answer: B.
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
A walker starts at the origin and travels along , then , then . How far from the origin is the walker?
Question 2
Starting at the origin, a particle travels along , then , then . Find the distance from the origin.
Question 3
A robot starts at and moves by , then , then . How far from is it?