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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 × b = b × c = c × a .

Markscheme

taking cross products with a,     M1

a × (a + b + c) = a × 0 = 0     A1

using the algebraic properties of vectors and the fact that a × a = 0 ,     M1

a × b + a × c = 0     A1

a × b = c × a     AG

taking cross products with b,     M1

b × (a + b + c) = 0

b × a + b × c = 0     A1

a × b = b × c     AG

this completes the proof

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3 - Core: Circular functions and trigonometry » 3.7 » The cosine rule.

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