Worksheets · Foundation and Higher

Column vectors and vector arithmetic

3 exam-style questions. Answers and the mark for each step are on the last page.

1. Question 1Non-calculator · 4 marks

   $A$ is the point $(1, 4)$ and $B$ is the point $(5, 1)$.

   (a) Write $\overrightarrow{AB}$ as a column vector. (1)

   (b) Write $\overrightarrow{BA}$ as a column vector. (1)

   (c) $\overrightarrow{AC} = 2\overrightarrow{AB}$. Find the coordinates of $C$. (2)
2. Question 2Non-calculator · 4 marks

   A particle is translated by $(4,-3)$, then by $(-2,5)$.

   (a) Find the resultant translation. (2)

   (b) Find the single translation that returns the particle to its starting point. (2)
3. Question 3Non-calculator · 5 marks

   $p\begin{pmatrix} 2 \\ 1 \end{pmatrix} + q\begin{pmatrix} 1 \\ -3 \end{pmatrix} = \begin{pmatrix} 7 \\ 0 \end{pmatrix}$, where $p$ and $q$ are numbers.

   (a) Find the values of $p$ and $q$. Give your answer as $(p, q)$. (3)

   (b) The vector $\begin{pmatrix} k \\ 6 \end{pmatrix}$ is parallel to $\begin{pmatrix} 2 \\ -3 \end{pmatrix}$. Find the value of $k$. (2)