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2025 HSC Mathematics Extension 1

Question 9:
Vectors

1 markvectors

The vectors , and have magnitudes , and . Given that , what is the angle between and ?

The supplied diagram of vectors a, b and c from a common point, including the angle theta between a and b.
The supplied diagram of vectors a, b and c from a common point, including the angle theta between a and b.

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

  1. , so .
  2. .
  3. , so and : option 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

Find the projection of onto .

See the step-by-step answer guide →

Question 2

Find if is parallel to .

See the step-by-step answer guide →

Question 3

Find the angle between and .

See the step-by-step answer guide →