| Date | None Specimen | Marks available | 7 | Reference code | SPNone.2.hl.TZ0.8 |
| Level | HL only | Paper | 2 | Time zone | TZ0 |
| Command term | Find | Question number | 8 | Adapted from | N/A |
Question
OABCDE is a regular hexagon and a , b denote respectively the position vectors of A, B with respect to O.
Show that OC = 2AB .
Find the position vectors of C, D and E in terms of a and b .
Markscheme
\({\text{OC}} = {\text{AB}} + {\text{OA}}\cos 60 + {\text{BC}}\cos 60\) M1
\( = {\text{AB}} + {\text{AB}} \times \frac{1}{2} + {\text{AB}} \times \frac{1}{2}\) A1
\( = 2{\text{AB}}\) AG
[2 marks]
\(\overrightarrow {{\text{OC}}} = 2\overrightarrow {{\text{AB}}} = \)2(b – a) M1A1
\(\overrightarrow {{\text{OD}}} = \overrightarrow {{\text{OC}}} + \overrightarrow {{\text{CD}}} \) M1
\( = \overrightarrow {{\text{OC}}} + \overrightarrow {{\text{AO}}} \) A1
= 2b – 2a – a = 2b – 3a A1
\(\overrightarrow {{\text{OE}}} = \overrightarrow {{\text{BC}}} \) M1
= 2b – 2a – b = b – 2a A1
[7 marks]
