4MA1/1HR Jan 2019, Question 22: Expressing Vectors in Terms of a and b
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks
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The question, in short
In regular hexagon ABCDEF, with AB→ = a and BC→ = b, and lines ABX and DCX straight, express vector EX using a and b in simplest form.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 4 marks
- 1Each interior angle of a regular hexagon is 120°
- 2ABX is a straight line, so angle XBC = 180 − 120 = 60°
- 3DCX is a straight line, so angle XCB = 180 − 120 = 60°
- 4So triangle BCX has three 60° angles and is equilateral, with BX = CX = BC = one side of the hexagon
- 5CX = CB + BX = −b + a = a − b
- 6DC is a side of the hexagon, so DC has the same length as CX and points the same way along the line DCX, giving DC = a − b
- 7ED is parallel to AB, the same length and the same direction, so ED = a
- 8EX = ED + DC + CX = a + (a − b) + (a − b)
- 9EX = 3a − 2b
Answer3a − 2b
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