# Maths edexcel vector question

Question lifted from past edexcel paper .

OAN OMB and APB are straight lines. M is the midpoint of OB.
OA=a. Vector
OB=b. Vector.
AP(vector)=k x AB(vector) where k is a scalar quantity.

Given that MPN is a straight line find the value of k

Thanks
I was doing that yesterday! Still working it out!
Something simple I'm missing..
Can I add a pic to the topic
Original post by Dm998
Question lifted from past edexcel paper .

OAN OMB and APB are straight lines. M is the midpoint of OB.
OA=a. Vector
OB=b. Vector.
AP(vector)=k x AB(vector) where k is a scalar quantity.

Given that MPN is a straight line find the value of k

Thanks

I can't do this... Have you got the question down completely? Could you post a picture of it?

Also, you have to post what you've worked out/tried so far before people can help you.
The answer is 2/5 but I keep getting -5/2
I'll add the question and working out if someone can tell me how to add an attachment
Original post by Dm998
I'll add the question and working out if someone can tell me how to add an attachment

There are insert image and attachment buttons above the box you type in when you post.
Not on my screen
Original post by ada_786
The answer is 2/5 but I keep getting -5/2

How are you tackling it?
Working out MN And PN as well as PM
Original post by Dm998
Not on my screen

https://imgur.com/b7PDxSM

This is the question? (you left out AN=2OA in your original post).
How can you work out any vectors involving P?
You can thank @ghostwalker
AB=b-a
MN=-0.5b+a+3a
MN=4a-0.5b
MP=-0.5b+a+k(b-a)
MP=-0.5b+a+kb-ka
4/1-k=-0.5/-0.5+k (number of As in MN divided by As in MP = no. Bs in MN/Bs in MP)
8/2-2k=-1/-1+2k
8(-1+2k)=-1(2-2k)
-8+16k=-2+2k
14k=6
k=6/14
k=3/7
Hope that helps
(edited 5 years ago)
AB = AO+OB
AB = -a+b
MN = MO+OA+AN
MN = -0.5b+a+2a
MN = 3a-0.5b
MP = MO+OA+AP
MP = -0.5B+a-ka+kb
NM = -3a+0.5b
NP = -2a+k(-a+b)
NPM is a straight line, so,
x × NP = NM
k = 2/5

Little late but correct
(edited 4 years ago)
Original post by Pro student
AB = AO+OB
AB = -a+b
MN = MO+OA+AN
MN = -0.5b+a+2a
MN = 3a-0.5b
MP = MO+OA+AP
MP = -0.5B+a-ka+kb
NM = -3a+0.5b
NP = -2a+k(-a+b)
NPM is a straight line, so,
x × NP = NM
k = 2/5

Little late but correct

Can you please explain the last step ?Exactly how did you get the 2/5 . I do get other steps though
Original post by Dm998
Question lifted from past edexcel paper .

OAN OMB and APB are straight lines. M is the midpoint of OB.
OA=a. Vector
OB=b. Vector.
AP(vector)=k x AB(vector) where k is a scalar quantity.

Given that MPN is a straight line find the value of k

Thanks

-3a+1/2b = x(-2+k(a-b))
-3a+1/2b = -2xa-kxa+kxb
inspect a and b:
2x+kx=3
2(1/2k)+k(1/2k)=3
1/k+1/2=3
1/k+1/2=3
k=2/5