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Vectors in two and three dimensions — Question 269

Original QCE Vault practice · 5 marks

Q269 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 269 (5 marks)

Let A, B and C be noncollinear points with position vectors a,b,c\mathbf a,\mathbf b,\mathbf c. M is the midpoint of BC. Define G by g=(a+b+c)/3\mathbf g=(\mathbf a+\mathbf b+\mathbf c)/3.
a)
Use vectors to prove G lies on AM and divides AM in the ratio AG:GM=2:1AG:GM=2:1.
[3 marks]
b)
Explain why the three medians of the triangle meet at G, even when the triangle is not in the xy-plane.
[2 marks]
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