(i)     Find the velocity vector, $\overrightarrow {{\rm{AB}}}$ .

(ii)    Find the speed of the particle.

Write down an equation of the line L .

(i) evidence of approach     (M1)

e.g. $\overrightarrow {{\rm{AO}}} + \overrightarrow {{\rm{OB}}}$ , ${\rm{B}} - {\rm{A}}$ , $\left( {\begin{array}{*{20}{c}} {9 - 6}\\ { - 6 + 2}\\ {15 - 10} \end{array}} \right)$

$\overrightarrow {{\rm{AB}}} = \left( {\begin{array}{*{20}{c}} 3\\ { - 4}\\ 5 \end{array}} \right)$ (accept $\left( {3, - 4, 5} \right)$ )    A1     N2

(ii) evidence of finding the magnitude of the velocity vector     M1

e.g. ${\text{speed}} = \sqrt {{3^2} + {4^2} + {5^2}}$

${\text{speed}} = \sqrt {50}$ $\left( { = 5\sqrt 2 } \right)$     A1     N1

[4 marks]

correct equation (accept Cartesian and parametric forms)     A2     N2

e.g. ${\boldsymbol{r}} = \left( {\begin{array}{*{20}{c}} 6\\ { - 2}\\ {10} \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 3\\ { - 4}\\ 5 \end{array}} \right)$ , ${\boldsymbol{r}} = \left( {\begin{array}{*{20}{c}} 9\\ { - 6}\\ {15} \end{array}} \right) + t\left( {\begin{array}{*{20}{c}} 3\\ { - 4}\\ 5 \end{array}} \right)$

[2 marks]

This question was quite well done. Marks were lost when candidates found the vector $\overrightarrow {{\text{BA}}}$ instead of $\overrightarrow {{\text{AB}}}$ in part (a) and for not writing their vector equation as an equation.

In part (b), a few candidates switched the position and velocity vectors or used the vectors $\overrightarrow {{\text{OA}}}$ and $\overrightarrow {{\text{OB}}}$ to incorrectly write the vector equation.