# help with as maths vectors question

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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.

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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(Original post by

What have you worked out so far

**user342**)What have you worked out so far

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#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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#5

(Original post by

Is part a supposed to be 1/2(-a+b) instead of 1/2(a+b)?

**user342**)Is part a supposed to be 1/2(-a+b) instead of 1/2(a+b)?

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#6

(Original post by

I’ve done part a I just need help with part b.

**gabriela4**)I’ve done part a I just need help with part b.

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#7

(Original post by

no i think it was as originally stated.

**the bear**)no i think it was as originally stated.

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#8

(Original post by

Hm, maybe I drew the wrong diagram or something?

**user342**)Hm, maybe I drew the wrong diagram or something?

**OM**

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#9

(Original post by

no that is fine. now mark in the midpoint of AB (call it M) and connect it to O. then think about the vector

**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**
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**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**

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#11

(Original post by

ohh right but for some reason it doesn’t sit right with me that it’s positive, it just doesn’t make sense.

**gabriela4**)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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#12

1/2(a+b) is the average of A and B position vectors. So it gives the midpoint.

However, prefer Bears explanation :-).

However, prefer Bears explanation :-).

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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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(Original post by

1/2(a+b) is the average of A and B position vectors. So it gives the midpoint.

However, prefer Bears explanation :-).

**mqb2766**)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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#15

(Original post by

what does average position vector mean???

**gabriela4**)what does average position vector mean???

If you have two vectors

**a**and

**b**, the average is (

**a**+

**b**) / 2.

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(Original post by

If you had two numbers x and y, the average would be (x + y) / 2.

If you have two vectors

**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.
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#17

(Original post by

ohhhh tysm we didn't get taught a load of all this vectors stuff

**gabriela4**)ohhhh tysm we didn't get taught a load of all this vectors stuff

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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(Original post by

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.

**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.

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(Original post by

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

**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

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#20

(Original post by

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

**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

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