The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

help with as maths vectors question

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.

Scroll to see replies

Reply 1
Avatar for user342
user342
12
What have you worked out so far
Reply 2
Avatar for gabriela4
gabriela4
OP
13
Original post by user342
What have you worked out so far

I’ve done part a I just need help with part b.
Reply 3
Avatar for user342
user342
12
Is part a supposed to be 1/2(-a+b) instead of 1/2(a+b)?
(edited 3 years ago)
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.
Reply 5
Avatar for user342
user342
12
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
Reply 6
Avatar for user342
user342
12
Original post by the bear
no i think it was as originally stated.

26075009-A74D-40D7-9E9D-59191ED12345.jpegHm, maybe I drew the wrong diagram or something?
Original post by user342
26075009-A74D-40D7-9E9D-59191ED12345.jpegHm, 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
Reply 8
Avatar for user342
user342
12
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 :smile:
Reply 9
Avatar for gabriela4
gabriela4
OP
13
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.
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/instances/81715532/suck-it-up-buttercup.jpg
1/2(a+b) is the average of A and B position vectors. So it gives the midpoint.

However, prefer Bears explanation :-).
Reply 12
Avatar for gabriela4
gabriela4
OP
13
Original post by the bear

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.
Reply 13
Avatar for gabriela4
gabriela4
OP
13
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???
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.
Reply 15
Avatar for gabriela4
gabriela4
OP
13
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 :smile: we didn't get taught a load of all this vectors stuff
Original post by gabriela4
ohhhh tysm :smile: 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.
(edited 3 years ago)
Reply 17
Avatar for gabriela4
gabriela4
OP
13
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!!
Reply 18
Avatar for gabriela4
gabriela4
OP
13
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
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...

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you