October 2020 Paper 1 Q3
3 The points A and B have position vectors \(\mathbf{a} = \begin{pmatrix} 3 \\ 2 \\ -1 \end{pmatrix}\) and \(\mathbf{b} = \begin{pmatrix} -1 \\ 4 \\ 8 \end{pmatrix}\) respectively.
Show that the exact value of the distance AB is \(\sqrt{101}\). [3]
| Scheme | Marks | AO |
|---|---|---|
| \(\overrightarrow{AB} = \mathbf{b} - \mathbf{a} = \begin{pmatrix} -4 \\ 2 \\ 9 \end{pmatrix}\) | B1 | 2.1 |
| distance \(= \sqrt{(-4)^2 + 2^2 + 9^2} = \sqrt{101}\) | M1 | 2.1 |
| A1 | 2.1 | |
| [3] |
Notes
B1: AG
Soi Allow for \(\overrightarrow{BA}\) even if wrongly labelled
M1: Attempt to find magnitude of their displacement vector
A1: cao AG
Do not allow final mark when there are missing brackets eg \(-4^2 + 2^2 + 9^2\)