LZZ's answer to Tammy Chan's Junior College 2 H2 Maths Singapore question.
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Hope this is the correct answer!! Quite rusty to H2 math now
Date Posted:
4 years ago
The question asks for OADC as a parallelogram , so the positions of D and C should be swopped since the ordering of letters in the parallelogram is from one vertice the next adjacent vertice
Yeapp thx for pointing that out. So basically ABC will be a line cutting the parallelogram into half.
Yup, it's one of the parallelogram's diagonal.
So the 2nd equation should be :
r = (3 1 2) + μ(-3 -17 8)
Comparing the two, we can get 3 equations :
3 - 3 μ = -3 + 3λ ① → λ = 2 - μ
1 - 17μ = -17 + λ ②
2 + 8μ = 8 + 2λ ③
Substitution will give μ = 1 and λ = 1
So OD = (3 1 2) + (-3 - 17 8)
= (0 -16 10)
Or OD = (-3 - 17 8) + (3 1 2)
= (0 -16 10)
depending on which equation is used.
So the 2nd equation should be :
r = (3 1 2) + μ(-3 -17 8)
Comparing the two, we can get 3 equations :
3 - 3 μ = -3 + 3λ ① → λ = 2 - μ
1 - 17μ = -17 + λ ②
2 + 8μ = 8 + 2λ ③
Substitution will give μ = 1 and λ = 1
So OD = (3 1 2) + (-3 - 17 8)
= (0 -16 10)
Or OD = (-3 - 17 8) + (3 1 2)
= (0 -16 10)
depending on which equation is used.
The other way (which I have written the steps in the comment section on the main qn page) would be to :
Let D(a,b,c) , recognise that CD = OA
(same magnitude and parallel since they are opposite sides of parallelogram OADC) and then compare coefficients to find OD
Let D(a,b,c) , recognise that CD = OA
(same magnitude and parallel since they are opposite sides of parallelogram OADC) and then compare coefficients to find OD
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