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2022 HSC Mathematics Extension 1

Question 11(a):
Vectors

2 marksvectors

For the vectors and , evaluate each of the following.

(i)

(ii)

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

  1. (i) .
  2. NESA (i): 1 mark for the correct answer .
  3. (ii) .
  4. NESA (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

For the vectors and , evaluate each of the following.

(i)

(ii)

See the step-by-step answer guide →

Question 2

Let and . Evaluate each of the following.

(i)

(ii)

See the step-by-step answer guide →

Question 3

For the vectors and , evaluate each of the following.

(i)

(ii)

See the step-by-step answer guide →