# help with as maths vectors question

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#1
OABC is a quadrilateral. Relative to point O, points A, B and C have position vectors
a b c , respectively.
(a) Show that the midpoint of AB has position vector
1/2 (a+b)
(b) Prove that the midpoints of sides OA, AB, BC and CO form the corners of a parallelogram.
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1 month ago
#2
What have you worked out so far
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#3
(Original post by user342)
What have you worked out so far
I’ve done part a I just need help with part b.
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1 month ago
#4
Is part a supposed to be 1/2(-a+b) instead of 1/2(a+b)?
Last edited by user342; 1 month ago
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1 month ago
#5
(Original post by user342)
Is part a supposed to be 1/2(-a+b) instead of 1/2(a+b)?
no i think it was as originally stated.
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1 month ago
#6
(Original post by gabriela4)
I’ve done part a I just need help with part b.
I would work out equations for the lines connecting the midpoints and then show that they're multiples of each other, and so they're parallel. Hope that helps
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1 month ago
#7
(Original post by the bear)
no i think it was as originally stated.
Hm, maybe I drew the wrong diagram or something?
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1 month ago
#8
(Original post by user342)
Hm, maybe I drew the wrong diagram or something?
no that is fine. now mark in the midpoint of AB (call it M) and connect it to O. then think about the vector OM
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1 month ago
#9
(Original post by the bear)
no that is fine. now mark in the midpoint of AB (call it M) and connect it to O. then think about the vector OM
Ah i was thinking of it as half of the vector A to B (which is wrong). Thanks
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#10
(Original post by the bear)
no that is fine. now mark in the midpoint of AB (call it M) and connect it to O. then think about the vector OM
ohh right but for some reason it doesn’t sit right with me that it’s positive, it just doesn’t make sense.
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1 month ago
#11
(Original post by gabriela4)
ohh right but for some reason it doesn’t sit right with me that it’s positive, it just doesn’t make sense.
https://memegenerator.net/img/instan...-buttercup.jpg
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1 month ago
#12
1/2(a+b) is the average of A and B position vectors. So it gives the midpoint.

However, prefer Bears explanation :-).
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#13
lool but i didn't even get that answer though, which is why i was asking because i kept on getting -a so i just gave up and decided to put positive a.
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#14
(Original post by mqb2766)
1/2(a+b) is the average of A and B position vectors. So it gives the midpoint.

However, prefer Bears explanation :-).
what does average position vector mean???
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1 month ago
#15
(Original post by gabriela4)
what does average position vector mean???
If you had two numbers x and y, the average would be (x + y) / 2.
If you have two vectors a and b, the average is (a + b) / 2.
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#16
(Original post by DFranklin)
If you had two numbers x and y, the average would be (x + y) / 2.
If you have two vectors a and b, the average is (a + b) / 2.
ohhhh tysm we didn't get taught a load of all this vectors stuff
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1 month ago
#17
(Original post by gabriela4)
ohhhh tysm we didn't get taught a load of all this vectors stuff
In a sense you were half right as
OM = 0A + AM
= OA + AB/2
= a + (b-a)/2
= (a+b)/2

You get the difference (b-a) when forming AB, but that is relative to point A. To make it relative to O you add a, and the midpoint M can be thought of as the average of a and b.
Last edited by mqb2766; 1 month ago
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#18
(Original post by mqb2766)
In a sense you were half right as
OM = 0A + AM
= OA + AB/2
= a + (b-a)/2
= (a+b)/2

You get the difference (b-a) when forming AB, but that is relative to point A. To make it relative to O you add a, and the midpoint M can be thought of as the average of a and b.
thank you!!
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#19
(Original post by user342)
I would work out equations for the lines connecting the midpoints and then show that they're multiples of each other, and so they're parallel. Hope that helps
i've tried to do that but idk it doesn't look right, i mean they all have 1/2 infront so i guess that's something (probably not though lol) but there are different letters, like sometimes a sometimes a+b sometimes c (if you know what i mean) so idk what to do, as that doesn't prove anything
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1 month ago
#20
(Original post by gabriela4)
i've tried to do that but idk it doesn't look right, i mean they all have 1/2 infront so i guess that's something (probably not though lol) but there are different letters, like sometimes a sometimes a+b sometimes c (if you know what i mean) so idk what to do, as that doesn't prove anything
If you do it correctly it will be obvious that you have a parallelogram. But if you're not going to post any kind of working there's not a lot anyone can do...
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