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2020 HSC Mathematics Extension 1

Question 6:
Vectors

1 markvectors

The vectors and are shown (two arrows from a common origin, pointing up-right and pointing right).

Which diagram below shows the vector ?

The supplied vectors a and b followed by the four candidate diagrams for a minus b.
The supplied vectors a and b followed by the four candidate diagrams for a minus b.
  1. Tip-to-tail sum diagram for
  2. Arrow representing
  3. Arrow parallel to with inconsistent sense
  4. Head-to-head: from the tip of to the tip of

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. By definition .
  2. Equivalently, if and share a start point, is the arrow from the tip of to the tip of .
  3. Option D matches that head-to-head construction. A is addition; B reverses the difference.
  4. Answer: D.

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

If and , what is ?

See the step-by-step answer guide →

Question 2

Vectors and start at the same point and end at and . Which statement describes ?

  1. The directed segment from to
  2. The directed segment from to
  3. The directed segment from to the midpoint of
  4. The directed segment from to
See the step-by-step answer guide →

Question 3

If and , find .

See the step-by-step answer guide →