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

Reply 1

ada_786

15

I was doing that yesterday! Still working it out!

Reply 2

Dm998

OP

3

Something simple I'm missing..
Can I add a pic to the topic

Reply 3

Toki the Dumdum

18

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.

Reply 4

ada_786

15

The answer is 2/5 but I keep getting -5/2

Reply 5

Dm998

OP

3

I'll add the question and working out if someone can tell me how to add an attachment

Reply 6

Toki the Dumdum

18

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.

OP

Not on my screen

OP

Original post by ada_786

The answer is 2/5 but I keep getting -5/2

How are you tackling it?

Reply 9

ada_786

15

Working out MN And PN as well as PM

Reply 10

Toki the Dumdum

18

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).

Reply 11

Dm998

OP

3

How can you work out any vectors involving P?

Reply 12

Y2_UniMaths

19

This questions has already been answered in a different thread https://www.thestudentroom.co.uk/showthread2.php?t=5262824
You can thank @ghostwalker

Reply 13

doctorwhonerd42

1

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 :smile:

(edited 5 years ago)

Reply 14

Pro student

3

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)

Reply 15

mahrunnasa

6

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

Reply 16

achoo7

1

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

Maths edexcel vector question

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