1. 1
   A drone starts at point A and moves according to the vector $\binom{4}{-3}$ to reach point B.

   (a)

   Find the magnitude of vector AB.

   [1 mark]

   • A5
   • B7
   • C1
   • D25

   (b)

   The drone then moves from B according to the vector $\binom{-1}{2}$ to reach point C. Find the vector AC.

   [1 mark]

   • A$\binom{3}{1}$
   • B$\binom{5}{-5}$
   • C$\binom{3}{-1}$
   • D$\binom{-3}{-1}$

   (c)

   Find the magnitude of vector BC $= \binom{-1}{2}$, correct to 1 decimal place.

   [1 mark]

   • A5.0
   • B1.4
   • C3.2
   • D2.2

   Total for question 1: 3 marks

2. 2
   In triangle OAB, $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$.

   (a)

   Find $\overrightarrow{AB}$ in terms of $\mathbf{a}$ and $\mathbf{b}$, simplifying your answer.

   [2 marks]

   (b)

   M is the midpoint of AB. Find $\overrightarrow{OM}$ in terms of $\mathbf{a}$ and $\mathbf{b}$, simplifying your answer.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Vectors $\mathbf{p} = \binom{6}{-2}$ and $\mathbf{q} = \binom{-3}{5}$.

   (a)

   Simplify $2\mathbf{p} - \mathbf{q}$, showing your working.

   [3 marks]

   (b)

   Find the magnitude of $\mathbf{p} + \mathbf{q}$, correct to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   In triangle OAB, $\overrightarrow{OA} = \mathbf{a}$ and $\overrightarrow{OB} = \mathbf{b}$. Point P lies on OA such that OP:PA = 2:1, and point Q lies on OB such that OQ:QB = 2:1.

   (a)

   Find $\overrightarrow{PQ}$ in terms of $\mathbf{a}$ and $\mathbf{b}$, simplifying your answer.

   [4 marks]

   (b)

   Given that $\overrightarrow{AB} = \mathbf{b} - \mathbf{a}$, show that PQ is parallel to AB.

   [4 marks]

   (c)

   R is the point such that $\overrightarrow{OR} = \mathbf{a} + \mathbf{b}$. Determine whether the midpoint of PQ lies on OR, and if so, state the ratio in which it divides OR.

   [5 marks]

   Total for question 4: 13 marks

End of questions