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mathematicsprinted 136 · PDF 137
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printed 136 · PDF 137
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Aitchison College Academic Resources.
i)
iii)
Identify the path from A to B.
4B = AC + CB
=a+b
AB =a+biU]
Identify the path from O toE.
OF = OA + AE
0]
A isthe midpoint of AB soOd = AB=at+b.
1
E isthe midpoint of AC so AE = 54C = z2.
Substitute these into the route for the path.
Of = 04 + HE = (a+b) +5
Simplify.
OE = 5a + bil]
The position vector of DisOD.
Identify a path from O to D that uses some of the paths you already know vectors for.
OD = OF + ED
a 1-—> 1 1
E isthe midpoint of AC so Ee = x4 = 52. Therefore ED must be equalto 73 +xb
where x is aconstant to be found.
EDis parallel to OF soED = HOE) = (50 ~ b}
1 3
za +xb= (3a - v)
(3)
Compare coefficients of a.
~ we
i] i]
i
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