Ask Singapore Homework?
Upload a photo of a Singapore homework and someone will email you the solution for free.
Question
junior college 2 | H2 Maths
One Answer Below
Anyone can contribute an answer, even non-tutors.
need help with part (ii). Already got (i) as (-3,-17,8)
Date Posted: 4 years ago
Views: 327
Let D(a,b,c)
CD = OA
(same magnitude and parallel since they are opposite sides of parallelogram OADC)
OD - OC = OA
(a b c) - (-3 -17 8) = (3 1 2)
(a + 3 b + 17 c - 8) = (3 1 2)
Comparing coefficients,
a + 3 = 3, b + 17 = 1, c - 8 = 2
a = 0, b = -16, c = 10
So D(0, -16, 10) . You can write OD accordingly
The exact area of OADC is just the magnitude of the cross product of OA and OC. You will get 6√138 units²
CD = OA
(same magnitude and parallel since they are opposite sides of parallelogram OADC)
OD - OC = OA
(a b c) - (-3 -17 8) = (3 1 2)
(a + 3 b + 17 c - 8) = (3 1 2)
Comparing coefficients,
a + 3 = 3, b + 17 = 1, c - 8 = 2
a = 0, b = -16, c = 10
So D(0, -16, 10) . You can write OD accordingly
The exact area of OADC is just the magnitude of the cross product of OA and OC. You will get 6√138 units²
See 1 Answer
done
{{ upvoteCount }} Upvotes
clear
{{ downvoteCount * -1 }} Downvotes
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
360 Tutoring Program