4MA0 Higher January 2017 Paper 4 Q15
15
Diagram NOT accurately drawn
\(\overrightarrow{AB} = \begin{pmatrix} 3 \\ 2 \end{pmatrix}\) and \(\overrightarrow{AC} = \begin{pmatrix} 4 \\ -1 \end{pmatrix}\)
(a) Find, as a column vector, \(\overrightarrow{BC}\) (2)
\(BCDE\) is a parallelogram.
\(\overrightarrow{CD} = 2\overrightarrow{AC}\)
(b) Find the length of \(CE\).
Give your answer correct to 2 decimal places. (3)
Give your answer correct to 2 decimal places. (3)
| Scheme | Marks |
|---|---|
| \(\begin{pmatrix} 4 \\ -1 \end{pmatrix} - \begin{pmatrix} 3 \\ 2 \end{pmatrix}\) oe | M1 |
| \(\begin{pmatrix} 1 \\ -3 \end{pmatrix}\) | A1 |
| (2) |
| Scheme | Marks |
|---|---|
| \(2\begin{pmatrix} 4 \\ -1 \end{pmatrix} - \begin{pmatrix} 1 \\ -3 \end{pmatrix}\left(= \begin{pmatrix} 7 \\ 1 \end{pmatrix}\right)\) | M1 |
| \(\sqrt{7^2 + 1^2}\) | M1 |
| 7.07 | A1 |
| (3) | |
| (5 marks) |
Notes
M1: Ft their \(\overrightarrow{BC}\) in (a)
For a correct expression for \(\overrightarrow{CE}\) or \(\overrightarrow{EC}\) in terms of column vectors
M1: Dep on first M1 awarded
ft their \(\overrightarrow{CE}\)
A1: 7.07106… rounded or truncated to at least 2DP
Accept \(\sqrt{50}\) or \(5\sqrt{2}\)