| Date | None Specimen | Marks available | 6 | Reference code | SPNone.1.hl.TZ0.8 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Show that | Question number | 8 | Adapted from | N/A |
Question
The vectors a , b , c satisfy the equation a + b + c = 0 . Show that a \( \times \) b = b \( \times \) c = c \( \times \) a .
Markscheme
taking cross products with a, M1
a \( \times \) (a + b + c) = a \( \times \) 0 = 0 A1
using the algebraic properties of vectors and the fact that a \( \times \) a = 0 , M1
a \( \times \) b + a \( \times \) c = 0 A1
a \( \times \) b = c \( \times \) a AG
taking cross products with b, M1
b \( \times \) (a + b + c) = 0
b \( \times \) a + b \( \times \) c = 0 A1
a \( \times \) b = b \( \times \) c AG
this completes the proof
[6 marks]
Examiners report
[N/A]
